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Given the vector A 4i 7j

Given v = .4i + 7j and w = 31 - 2), find the vector projection v onto w o projw = 21 + 6] o projwv = 21-4 O projwv = -71 - 61 projw = 61 - 3) projwv = -B1 + 4 Get more help from Chegg Solve it with our algebra problem solver and calculato the question is given 2 vectors A=4i+7j and B=5i+2j find the vector product AxB and express in terms of i,j,k? they want you to express as its unit vectors i,j,k and i worked out the product but dont know how to express as such. anybody ready to teach and help me ou What is the magnitude of the vector A=4i+7j-4k? The magnitude of a vector is the distance from the endpoint to the origin. The endpoint is described by the coefficients of your vector. In your case, the point is (4,7,-4) Given that point A has the position vector 4i + 7j and point B has the position vector 10i + qj, where q is a constant, find a) the vector AB in terms of q b) Given further that |AB| = 2√13, find two possible values of q showing detailed reasoning in your working Thank Given that point A has the position vector 4i + 7j and point B has the position vector 10i + qj, where q is a constant, find (a) the vector AB in terms of q. (b) Given further that AB = 2 (square root) 13 , find the two possible values of q showing detailed reasoning in your working

Solved: Given V = .4i + 7j And W = 31 - 2), Find The Vecto ..

  1. Now, write these results in a vector form to find the vector û = (0.8081, -0.3031, 0.5051). You can check whether the result is correct. If it is, the magnitude of your unit vector should be equal to 1
  2. Find the following information for each vector, if not provided in the question: Component form, linear combination, magnitude and direction angle. 9) -16i + 30j 10) -3i - 33
  3. Forces 2i + 7j, 2i - 5j + 6k, - i + 2j - k act at a point P whose position vector is 4i - 3j - 2k. asked Jan 4, 2020 in Vector algebra by AmanYadav ( 55.6k points) vector algebr
  4. A unit vector that points in the direction of the vector -4i + 7j can be written as? and how to calculate it when given the components of a vector. A short quiz will follow

the question is given 2 vectors A=4i+7j and B=5i+2j find

The given vector is: v = -3i-7j. The unit vector is found by dividing the vector by its magnitude. We have to find the magnitude first. So, The unit vector is: Therefor the last option is the correct answer. New questions in Mathematics. 10. Find the volume of the right cone pictured here. (Give your answer correct to 1 decimal place. Resultant vector, Explanation: Vector, Vector, Magnitude of vector A is, A = 3.6. Direction of vector B is, Let R is the vector having the magnitude of A and direction of B. So, Learn more, Vectors. brainly.in/question/914872 In order to find the unit vector u of a given vector v, we follow the formula. Let. The magnitude of v follows the formula. For this vector in the problem. Following the unit vector formula and substituting for the vector and magnitude. As such,

What is the magnitude of the vector A=4i+7j-4k? - Quor

Vectors Question Help - The Student Roo

You can put this solution on YOUR website! To calculate the norm of the vector use the following formula: where is the dot product of the given vector with itself Calculate the dot product of the radicand Multiply Add So Notice if we draw the vector we get Plot of the vector (black line) with the vector components (green where is the dot product of the given vector with itself Remember the dot product of the vector with itself is: Calculate the dot product of the radicand Multiply Add Simplify if possible So Check: Lets use Pythagorean's Theorem to check our work Notice if we draw the vector we get Plot of the vector (black line) with the vector components (green Answer to: Given vector A= 5i-2j, vector B= -4i+7j and vector F= vector A - 5(vector B). What is the magnitude of vector F? What is the direction.. given u= 2i+j-k and v=i-7j+2k find (u*v)v. asked Oct 31, 2017 in CALCULUS by The initial and terminal points of a vector are given.Write a linear combination of the standard unit vectors i and j. Find the magnitude and direction angle θ, to the nearest tenth of a degree, for the given vector v. v = -4i - 3j. asked Jul 17, 2016 in. At time t = O. a second boat B is at the point with position vector (— Given that the velocity of B is (3i + 4j) m s- (c) show that A and B will collide at a point P and find the position vector of P. (5) Given instead that B has speed 8 m s. I and moves in the direction of the vector (3i + 4j), (d) find the distance of B from P when 7 s

Operations on vectors - addition, multiplication by a number. Let's consider a vector v whose initial point is the origin in an xy - coordinate system and whose terminal point is . We say that the vector is in standard position and refer to it as a position vector. Note that the ordered pair defines the vector uniquely Click hereto get an answer to your question ️ If 4i + 7j + 8k, 2i + 7j + 7k and 3i + 5j + 7k are the position vectors of the vertices A,B and C respectively of triangle ABC . The position vector of the point where the bisector of angle A meets BC Unit Vector Formula Questions: 1) Given a vector , find the unit vector .Express it in both bracket format and unit vector component format. Answer: The magnitude of the vector is: The magnitude can now be used to find the unit vector Initials Given the following vectors A and B, A = 4i + 7j B-3i-6j, find the magnitude and direction for vector C- 5A-2B Find the resultant vector Ř A B C 6. A + B + C. 15.0 m,..

determine vector of position of C if vector of position of A,B in triangle ABC are given. vec pA=4i+7j vecpB=2i-j vec pG=4i+4j g is centroid point 1 Educator answer Mat Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor

Pure Maths Position vectors - The Student Roo

Given vectors A = -4.8i + 6.8j and B = 9.6i + 6.7j, determine the vector C that lies in the xy plane, is perpendicular to B, and whose dot product with A is 20.0. The correct answer should be : -1.4i + 2.0j I did find the dot product by: i-> (-4.8)*9.6= -46.08 j-> 6.8*6.7 = 45.56 (-46.08) + 45.56 = -0.52 but then it doesn't help me with the problem so I sketched the two vectors in the xy plane. A unit vector is the equivalent vector of an original vector that has a magnitude of 1. In other words, it has the same direction as your original vector but the total magnitude is equal to one. Since the unit vector is the originally vector divided by magnitude, this means that it can be described as the directional vector

Unit Vector Calculato

general treatment will be given later on (see Chapter 8). Definition 4.4. Given any square matrix A ∈ M n(C), acomplexnumberλ ∈ C is an eigenvalue of A if there is some nonzero vector u ∈ Cn,suchthat Au = λu. If λ is an eigenvalue of A,thenthenonzero vectors u ∈ Cn such that Au = λu are called eigenvectors of Once the ideas of scalar (dot) product and vector (cross) product for two vectors has been introduced, it is then possible to consider certain products of three or more vectors where, in some cases, there may be a mixture of scalar and vector products. 8.4.1 THE TRIPLE SCALAR PRODUCT DEFINITION 1 Given three vectors a, b and c, expressions such a So, the area of the given triangle is (1/2) √165 square units. Problem 3 : If a vector, b vector, c vector are position vectors of the vertices A, B, C of a triangle ABC, show that the area of the triangle ABC is (1/2) | a × b + b × c + c × a| vector. Also deduce the condition for collinearity of the points A, B, and C. Solution This is true of many physics applications involving force, work and other vector quantities. Perpendicular vectors have a dot product of zero and are called orthogonal vectors. Figure 1 shows vectors u and v with vector u decomposed into orthogonal components w 1 and w 2 Click here to get an answer to your question ️ Let vector a = 4i +3j and b vector = 3i + 4j . (A)Find the magnitudes of (a) a vector (b) b vector (c) a v

Given vector A = 2i + 3j + 6k, vector B = i + j - 2k and

vector a = 4i + 3j, vector b = 3i + 4j find the magnitude of a find the magnitude of b find the magnitude of a+b find the magnitude of a-b a = 4i + 3j , b = 3 Given that point A has the position vector 4i + 7j and point B has the position vector 10i + qj, where q is a constant, find (a) the vector AB in terms of q. (2) (b) Given further that AB 2 13. Introduction to Vector Calculus (37) is 2 2 2 4i 2j 3k . i 3j 2kˆ ˆ ˆ ˆ ˆ ˆ 1 3 2 = 16 8 14 14 7 and component of a along i 3j 2k ˆ ˆ is = 2 2 2 4i 2j . i 3j 2kˆ ˆ ˆ ˆ ˆ 2 1 3 2 14 = 14 7 Q.15: Calculate the unit vector, which is normal to the surface = x y xy 3xyz2 2 at the point (1, 1, -1). Solution : Her 10.Define cross product or vector product of any two vectors. Solution; If a and b are any two vectors and θ be the angle between Them & η unit vector perpendicular to both a & b , then, a X b = | a | | b | η Sinθ a θ b η 11. If the position vectors of P & Q are 3i + 2j - 7k and 4i + 7j - 11k Then, Find PQ & |PQ| Given the two nonparallel vectors a = -4i + 3j and b = 2i - j and another vector r = 6i - 7j, find scalars k and m such that r = ka + mb. Students also viewed these Calculus questions Given the two nonparallel vectors a = 3i - 2j and b = -3i 4j and another vector r = 7i - 8j, find scalars k and m such that r = ka + mb

Every nonzero vector has a corresponding unit vector, which has the same direction as that vector but a magnitude of 1. To find the unit vector u of the vector you divide that vector by its magnitude as follows: Note that this formula uses scalar multiplication, because the numerator is a vector and the denominator [ Verify if the point having position vector 4i^-11j^+2k^ lies on the line r¯=(6i^-4j^+5k^)+μ(2i^+7j^+3k^) Maharashtra State Board HSC Science (General) 12th Board Exam. Question Papers ∴ The given point lies on the given line. Concept: Vector and Cartesian Equations of a Line.

Given magnitude and direction and trying to find a vector, first use this equation. divide it by the magnitude. Given magnitude and direction and trying to find a vector, after using the distance equation, you do this to the number. (Given Magnitude/Found Magnitude)(Points) v=-4i-7j. OTHER SETS BY THIS CREATOR. Stat 123 GEQ/LEQ 10 Terms. If a = 9i+7j and b = 8i+3j find (a) a+b (b) a−b Your solution Answer (a) Simply add the respective components: 17i+10j, (b) Simply subtract the respective components: i+4j Now consider the special case when r represents the vector from the origin O to the point P(a,b). This vector is known as the position vector of P and is shown in Figure 26 Find the magnitude and direction angle θ, to the nearest tenth of a degree, for the given vector v. v = -4i - 3j asked Jul 17, 2016 in PRECALCULUS by anonymous pre-cal

A ray of light is incident on a plane mirror along a vector a i + b j − c k. The normal on incidence point is along 2 i + j .find a unit vector along the reflected ray. Mediu The scalar product of the standard basis vectorsBy assumption the standard basis vectors i, j and k aremutually perpendicular, and of magnitude one. Hence bydefinition of the scalar product 1. i · i = j · j = k · k = 1; 2. i · j = i · k = j · k = 0. The component of a vector parallel to a given vector 3

With respect to a fixed origin O, the lines Il and 12 are given by the equations r = (3i+j+ 17k) 5k) where and u are scalar parameters. (a) Show that Il and 12 meet and find the position vector of their point of intersection. (b) Show that Il and 12 are perpendicular to each other. The point A has position vector 5i + 7j + 3k Find a unit vector that has the same direction as the given vector. −3i 7j 1 See answer Tommu7r1ikaypanity is waiting for your help. Add your answer and earn points. Edufirst Edufirst The unit vector has the same direction of the given vector but its magnitude is 1 Given a vector A = 2i + 3j and a vector B = i + j. The component of the vector A along B is (a) 1/(2)½ (i + j) (b) 3/(2)½ (i + j) (c) 5/(2)½ (i + j) (d) 7/(2)

Find the vector equation of the plane passing through the

  1. The vector product mc-TY-vectorprod-2009-1 One of the ways in which two vectors can be combined is known as the vector product. When we calculate the vector product of two vectors the result, as the name suggests, is a vector. In this unit you will learn how to calculate the vector product and meet some geometrical appli-cations
  2. Express the resultant vector as a linear combination of unit vectors i and j. 14) u = 2i - 3j g = 4i + 7j Find: 6u - 5g 15) Given: P = (-3, 10) Q = (-1, -2) Find the vector opposite PQ 16) Given: A = (-3, -10) B = (8, -9) Find: 10AB Draw a diagram to illustrate the horizontal and vertical components of the vector. Then find the magnitude of.
  3. After having gone through the stuff given above, we hope that the students would have understood, How to Prove the Given 4 Vectors are Coplanar Apart from the stuff given in How to Prove the Given 4 Vectors are Coplanar, if you need any other stuff in math, please use our google custom search here
  4. Question 7: Two vectors u and v have magnitudes equal to 2 and 4 and direction, given by the angle in standard position, equal to 90° and 180° respectively. Find the magnitude and direction of the vector 2 u + 3 v Solution to Question 7: Let us first use the formula given above to find the components of u and v
  5. so far when I've told you about the dot and the cross products I give you the definition as the magnitudes times either the cosine of the sine of the angle between them but what if you're not given the vectors visually and what if you're not given the angle between them how do you calculate the dot in the cross products so let's say well let me give you the definition that I've given you.
  6. al point (−2,4) u = −5 / √61, 6 / √61 Write the vector as a linear combination of the unit vectors i and j

Find the component form of the vector given its magnitude and the angle it makes with the positive x-axis Find the component form of the sum of two vectors with the given direction angles Use the Law of Cosines to find the angle between two vectors Word Problems - use vectors to find speed and direction. 1 Two vectors are given as a = i +2 j +2 k and b =2 i +4 j +2 k. Vector c which satisfies the relation a-b+c=3i is: a) i+3j c) ) -i+5j b) - i +j d) 4i+2j 2 For any two vectors A and B, if A.B =0 then the angle between them is a) Zero c) 30 degree b) 90 degree d) 180 degree 3 For A = 3j - 4k and B = -5j + 4k, B.A is: a) -31 c) -15i + 16 j b.

A unit vector that points in the direction of the vector

Any vector in R3 may be written uniquely as a combination of these three vectors. For example, the vector ~v= 3^{ 2^|+4^k represents the vector obtained by moving 3 units along the x-axis, two units backwards along the y-axis and four units upwards. If we imagine moving the vector so it's tail is at the origin then the endpoint Pdetermines. In addition to finding a vector's components, it is also useful in solving problems to find a vector in the same direction as the given vector, but of magnitude 1. We call a vector with a magnitude of 1 a unit vector. We can then preserve the direction of the original vector while simplifying calculations The Vector Product 9.4 Introduction In this Section we describe how to find the vector product of two vectors. Like the scalar product, its definition may seem strange when first met but the definition is chosen because of its many applications. When vectors are multiplied using the vector product the result is always a vector Free Online Scientific Notation Calculator. Solve advanced problems in Physics, Mathematics and Engineering. Math Expression Renderer, Plots, Unit Converter, Equation Solver, Complex Numbers, Calculation History Think of the geometric representation of a vector sum. When two vectors are summed they create a new vector by placing the start point of one vector at the end point of the other (write the two vectors on paper). Now, imagine if vectors A and B both where horizontal and added. They would create a vector with the length of their two lengths added

Given a point -4,-3 such that its position vector a→ is given by a→ = -4 i ∧- 3 j∧ Then, a→ = -42 + -32 = 16 + 9 = 25 = 5. Q2. Answer : Given a position vector a→ of a point 12, n such that, a→ = 12 i∧ + n j∧ Then, a→ = 122 + n2 Also , a→ = 13 (given) Thus, we get, 122 + n2 = 13⇒ 122 + n2 = 169⇒ n2 = 169 - 144⇒ n2. Solved: Find the angle between u and v in radians. u = -4i + 10j - 6k, v = 10i + 7j - 9k a)1.57 b) 0.47 c) 1.35 d) 1.10 By signing up, you'll get.. Determine the components of both points of the vector. Every vector can be numerically represented in the Cartesian coordinate system with a horizontal (x-axis) and vertical (y-axis) component. It is written as an ordered pair =<, >.If you are given a vector that is placed away from the origin of the Cartesian coordinate system, you must define the components of both points of the vector what I want to do in this video is explore the idea of a unit vector and a unit vector is just a vector that goes in a particular direction that has a magnitude that has a magnitude of 1 so let's take an example let's say that I have the vector let's say the vector a and it in the horizontal direction for every three that it moves in the vertical direction it moves up four it moves up four so.

Solved: Given A = 4i + 2j, B = 2i + 2j + 2k And C = 4i + 4F

WB19. i) Find the magnitude of each vector . ii) Find the angle between each vector and the positive x-axis. 4i+5j -4i+7j . 6i-2j -3i-5j . WB20. Vector a has magnitude 10 and makes and angle of 30° with j as shown . Find . a in i, j . format . Vector . b has magnitude 6 and makes and angle of 45° with . i . Given that . a and b . have the same starting point. b) Find . b in i, j . forma A vector that has a magnitude of 1 is a unit vector. It is also known as Direction Vector. Learn vectors in detail here. For example, vector v = (1,3) is not a unit vector, because its magnitude is not equal to 1, i.e., |v| = √(1 2 +3 2) ≠ 1. Any vector can become a unit vector by dividing it by the magnitude of the given vector Homework Help - Finding a Vector when given two points, and then finding a unit vector in the same direction. Ask Question Asked 10 years, I know that to find a unit vector, we first find the length/magnitude of the given vector, and multiply $$1/\sqrt{magnitude}$$ by the original vector Guide - how to use vector magnitude calculator To find the vector magnitude: Select the vector dimension and the vector form of representation; Type the coordinates of the vector; Press the button Calculate vector magnitude and you will have a detailed step-by-step solution

Free vector projection calculator - find the vector projection step-by-step This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy Exercise 11A : VECTOR EQUATION OF A LINE 1. State the vector equation of the straight line which is parallel to 2i + 5j + k and which passes through the point with position vectors 3i - j + 2k. 2. State the vector equation of the straight line which passes through the point A, position vector i + 2k and which is parallel to 4i - j + k. 3 An online calculator to calculate the magnitude and direction of a vector from it components.. Let v be a vector given in component form by v = < v 1, v 2 > The magnitude || v || of vector v is given by || v || = √(v 1 2 + v 2 2) and the direction of vector v is angle θ in standard position such that tan(θ) = v 2 / v 1 such that 0 ≤ θ < 2π. Use of the calculator to Calculate Magnitude. (d) a unit vector parallel to 3A - 2B + 4C (3A - 2B + 4C) . 398-½ 3. The position vectors of points P and Q are given by, r 1 = 2i + 3j - k, r 2 = 4i-3j+2k. Determine PQ in terms of rectangular unit vector, i, j and k and find its magnitude. (2i - 6j + 3k), 7 4

Ex 10.2, 11 (Method 1) Show that the vectors 2 ̂ − 3 ̂ + 4 ̂ and − 4 ̂ + 6 ̂ − 8 ̂ are collinear.Two vectors are collinear if they are parallel to the same line. Let ⃗ = 2 ̂ − 3 ̂ + 4 ̂ and ⃗ = -4 ̂ + 6 ̂ - 8 ̂ Magnitude of ⃗ = √(22+(−3)2+42)| ⃗ | = √(4+9+16) = √2 Given that OA=3i-2j+k and OB=4i+j-3k. Find the distance between points A and B to 2 decimal places. 15. Point T is the midpoint of a straight line AB. Given that the position vectors of A and T are i-j+k and 2i+1 #1/2# k respectively, find the position vector of B in terms of i, j and k. 16. Given that qi+ #1/3#j+#2/3# k is a unit vector, find. Press the button Find vector projection and you will have a detailed step-by-step solution. Entering data into the vector projection calculator. You can input only integer numbers or fractions in this online calculator. More in-depth information read at these rules The edited title and question were significantly more readable. When rendered, the command times is displayed as the appropriate cross product symbol

The point A has position vector a = 2i +2j + k and the point B has position vector b = i + j - 4k, relative to an origin O. (a) Find the position vector of the point C, with position vector c, given by c = a + b. (1) (b) Show that OACB is a rectangle, and find its exact area. (6) The diagonals of the rectangle, AB and OC, meet at the point D AC. The vector * OA is parallel to the vector i and four times its length so * OA= 4i. Similarly * AC= 3j. Thus the vector * OC may be written as * OC= 4i+3j. This is known as the 2-dimensional component form of the vector. In general every vector can be written in component form. This package will consider only 2-dimensional vectors The unit vector parallel to the resultant of vectors a=4i+3j+6k and b=-i+3j-8k Get the answers you need, now

A 100 meter dash is run on a track in the direction of the vector v = 4i + 7j. The wind velocity w is 5i + j km/hr. The rules say that a legal wind speed measured in the direction of the dash must not exceed 5 km/hr. Find the component of w which is parallel to v. Homework Equations The Attempt at a Solution I have no idea to solve this proble If the component points in the negative direction of one of your axes, it is given a negative sign. For example, in a 2-D plane, if a component points to the left or downwards, it is given a negative sign. For example, let's say that we have a vector with a magnitude of 3 and a direction of 135 o relative to the horizontal Initials Given the following vectors A and B, A = 4i + 7j B-3i-6j, find the magnitude and direction for vector C- 5A-2B 2. Given the vectors u = 2i + 3j and v = -3i - 2j (a).. A unit vector that points in the direction of the vector -4i + 7j can be written as? dr.two. Question. A unit vector that points in the direction of the vector -4i + 7j can be written as? Details Purchase An Answer Below flash243. Answer: Answer Price:. Q.2. If the sum of two unit vector is a unit vector, prove that the magnitude of their difference is √3. Q.3. Let a = 4i + 5j - k , b = i - 4j + 5k and c = 3i + j - k. Find a vector d which is perpendicular to both a and b and satisfying d.c = 21. Q.4

Given v 3i-j and w 4i+ 7j. find the angle between v and w What is the angle between v and w? Then round to the nearestf tenth as Type your answer in degrees. Do not round until the final answer Mar 19 2021 06:40 AM. Expert's Answer. Solution.pdf Next Previous. Two forces, (4i — 5j) N and (pi + qj) N, act on a particle P of mass m kg. The resultant of the two forces is R. Given that R acts in a direction which is parallel to the vector (i — 2j), (a) find the angle between R and the vector j, (3) (b) show that2p+q+3 = 0. (4

Given a vector m = 5i + 6j +3 in the orthogonal system, determine a parallel vector to this vector and point in the opposite direction. Solution. Let's consider a vector n that is a parallel vector to the given vector m. The vector n can be expressed as: n = k *m. n = k *(5i + 6j +3) Where k is a scalar multiple of the vector m (i) Find, in vector form, an equation for the line passing through A and B. I can't seem to get the answer. The given one is r = (7 -8 7) + t(1 -5 1) (ii) Find the position vector of the point P on the line AB such that OP is perpendicular to AB. (iii) Show that the line R - (8i - 5j +2k) + λ(i - 10j +4k) does not intersect the line AB

But the vector w = is a unit vector because The basic unit vectors are i = (1, 0) and j = (0, 1) which are of length 1 and have directions along the positive x-axis and y-axis respectively. To find a unit vector with the same direction as a given vector, we divide by the magnitude of the vector Divide this vector by its magnitude Unit vector = 4i - 3j / √[(4²) + (-3)²] = 4i - 3j / √25 = (4i - 3j) / 5-4^2+3^2 = 5^2 So, the unit vector is (1/5)(4i - 3j

Example \(\PageIndex{1B}\): Drawing a Vector with the Given Criteria and Its Equivalent Position Vector. Find the position vector given that vector \(v\) has an initial point at \((−3,2)\) and a terminal point at \((4,5)\), then graph both vectors in the same plane. Solution. The position vector is found using the following calculation R is parallel to the vector (I - 2j), Find the angle between R and the vector j. Show that 2p + q + 3 =0. Given also that q = 1 and that P moves with an acceletion of magnitude 8root5 m/s. Find the value of If vector B is added to vector A, the result is 6i +; j. If B is subtracted from A, the result is -4i +; 7j. What is the magnitude of A The definition is the same with everything; basically a number.Whether it's restricted to real or complex numbers is usually clear from context

Solved: This Question: 2 Pts Let V= -5i +5j And W= -1-4jSolved: Vector A = 4i + 3j - 2k And Vector B = 2i - 3j + 2

For v=-3i-7j, find the unit vector in the same direction

  1. Express the vector in terms of I and j. A quarterback releases a football with a speed of 38 ft per second at an angle of 30 deg with the horizontal. V = ‖ v ‖ cos θi + ‖ v ‖ sin θj V = 38 cos30i + 38 sin 30j V = 38( √ 3 2 ¿ i + 38 ( 1 2 ) j V = 19 √ 3 i + 19j Unit 4 HW Set 8 Ellipse x ² a ² + y ² b ² = 1 The vertices are.
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  3. Find a vector equation and the corresponding cartesian equation for each of the following lines. a) The line L1 is parallel to the vector 2i + 3k + 2k and passing through the point with position vector -i + 4j + 5k. b) The line L2 passes through the point with position vector 4i + 5j - k and the origin. 9
  4. Example 16 Find the projection of the vector ⃗ = 2 ̂ + 3 ̂ + 2 ̂ on the vector ⃗ = ̂ + 2 ̂ + ̂. Given ⃗ = 2 ̂ + 3 ̂ + 2 ̂ ⃗ = 1 ̂ + 2 ̂ + 1 ̂We know that Projection of vector ⃗ on ⃗ = /(| ⃗| ) ( ⃗. ⃗)Finding ⃗. ⃗( ⃗. ⃗) = (2 × 1) + (3 × 2)
  5. 1 Given that the point A has position vector 3i + 4j and the point B has position vector -4i + 7j (a) Find the vector (b) Find (Total for question 1 is 4 marks) (2) |⃗AB| (2) ⃗AB 2 Given that | 3i + kj | = 3 17 Find the value of k (Total for question 2 is 2 marks) 3 Given that the point A has position vector -5i + 7j and the point B has position vector -8i + 2j.
  6. al point.The vector with initial point A= (
`A=4i+4j-4k and B=3i+j4k`, then angle between vectors AA boat is moving with velocity 3i+4j with respect to

In order to obtain a vector n normal to the plane, we compute the cross product of the vectors h1; 3; 1iand h1;1;1ithat are parallel to the given lines. n = i j k 1 3 1 1 1 1 = 2i 2j+ 4k: In fact, as a normal vector we can take another vector parallel to the latter one: i+ j 2k. Therefore, the plane has the equation (x 0) + (y 3) 2(z+ 2) = 0 This second form is often how we are given equations of planes. Notice that if we are given the equation of a plane in this form we can quickly get a normal vector for the plane. A normal vector is, \[\vec n = \left\langle {a,b,c} \right\rangle \] Let's work a couple of examples Find the volume of the parallelopiped whose coterminus edges are given by vectors 2i+3j-4k, 5i+7j+5k and 4i+5j-2k - Mathematics and Statistics. Sum. Find the volume of the parallelopiped whose coterminus edges are given by vectors `2hati+3hatj-4hatk, 5hati+7hatj+5hatk and 4hati+5hatj-2hatk The magnitude of a vector is its size. It can be calculated from the square root of the total of the squares of of the individual vector components $\vec{a}$ is a vector which you can represent as a line from (0,0) to the point (3,4). By Pythagoras the length of the line is 5. Joining any two points along that line will give you a vector in the same direction as $\vec{a}$. You want a vector with magnitude 27, so you can just join (0,0) to the point 27/5*(3,4) i.e. to (81/5, 108/5)

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