Let i = 3 . Find the the angles 01.02,03 that ū makes with respectively, či...
3. If ū= 4.2,1 and ū= -2.2.1), find a vector in R3 that is orthogonal to both ū and . Answer: 4. Let A, B and C respectively denote the points (1,1,2), (-3, 2, 1) and (4, -2, -1). Find AB, AC and AB X AC. Answer: AB= AC = 1. AB X AC = 5. (a) Find the equation of the plane containing the points A, B and C above. Answer: (b) Check that your answer to (a) above...
Given the following vectors: ū= 3 ū= W = > (a) Find the projection of ū onto ū. BOX YOUR ANSWER. (b) Find the projection matrix of the projection in part (a). BOX YOUR ANSWER. (c) Find the projection of ū onto the subspace V of R3 spanned by ✓ and W. (You may use MATLAB for matrix multiplication in this part, but you must provide the expressions in terms of matrices.) BOX YOUR ANSWER. (d) Find the distance from...
5 3 1 Let ū = < 2,-3> V = <-2,0 > w = <3,3 > Graph vectors ū, ū, and w in standard position with corresponding terminal points, A, B, and C, respectively. (72 point) What is the length of the altitude of AABC from vertex A? (72 point) -5 -3 -1 -1 0 1 3 5 -3 -5
2. Let ū= (3,1, -7), ã = (1,0,5). (a) Find the vector component of u along a. (b) Find the vector component of ü orthogonal to ä. (c) Find the angle between u and , in degrees.
1. Let {ü, 7,w, i}, where u = (3,-2), v = (0,4), ū = (-1,5) and i = (-6,4). Find the components of the resultants obtained by doing the following linear combinations. a. r = 2ū - 40 b. š= 3ū – +20 +
3. Let A and B be any nxn matrices. Suppose ū is an eigenvector of A and A+B with corresponding eigenvalues 1 and p. Show that ū is also an eigenvector for B and find an expression for its corresponding eigenvalue. [2]
1. Let ū= (2,4,-1), v = (3.-3,-1) (a) Compute: x ū (b) Compute: ü x 7 (c) Is the cross product commutative? If not, what is it instead? 2. Let A = (7, -11,3), B = (1,9, -3), C = (-6,3, -2), D= (0,-8, 12), E = (1, -13,2) (a) Give the vector equation of a line passing through the points A, B. (b) Find the equation of the plane containing the points C,D,E. (c) Find the point of intersection...
Problem 3. For e 0,7), let Le CRP be the line that makes angle with the positive c-axis. Let To: R2 → R2 be the reflection about Le. Let Ao e R2,2 be the matrix representation of To. a) Find A0, A1/2, and Af/4. For each answer, justify by drawing the images of ēj = (1,0) and ē, = (0,1) under the corresponding reflection. b) Find an orthonormal basis B = (v1, U2) such that To = CT1/ 6C Justify...
If cos a = 0.972 and sinB = 0.098 with both angles' terminal rays in Quadrant-I, find the values of (a) cos(B – a) (b) sin(a - b) = Your answers should be accurate to 4 decimal places.
Let ū = [1,-1, 1], v = (-2,-1, 3] and W = (-1, 2, 2). Find (u x D) • w O Does not exist 7 -14 10