4. Let ū, w be vectors. Prove the Parallelogram Law: || + 2011? + || D...
5. Let ū and w be vectors in R3. Prove that (ö - w) x (v + 2) = 2(vx w).
3. Let ū and ū be vectors. Prove that ū x ū is orthogonal to both ū and v.
(1 point) Let ū = 5, 0 = U2 = -4 If possible, express ū as a linear combination of the vectors ū, and ū2. Otherwise, enter DNE. For example, the answer ū = 471 +5ū2 would be entered 4v1 + 5v2. w = 1v1+26/5v2
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
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...
6. Displacement vectors 7 , ū, V, and ū are given below. In the appropriate diagram, draw (a) the projection of 7 onto ū (b) the projection of ū onto ū (c) the projection of ū onto ū. ū ū ū 2 f V w
problem 1 and problem 2 please , thankyou very much PROBLEM 1 (25%) Find: Let: ū= (1,-1,-2) v = (-2,-2,3) w = (3,-1,1) (a) The angle between ū and w (b) Orthogonal projection of u against v (c) The area of parallelogram formed by u dan v (d) The volume of parallelpiped shaped byū, v, dan w PROBLEM 2 (15%) Determine if these sets of points are coplanar: (a) A(1,1,-3); B(0,1,-2); C(-3, 1, 1); D(2, 1, -4) (b) E(1,1,-1); F(0,1,1);...
15. [9 points) Consider the vectors v and w which determine the parallelogram in the figure, below, with the lengths of selected segments given. Use the Parallelogram Identity and the Polarization Identity, both on Page 32, to help determine the angle between the vectors v and w. Give your answer in degrees, rounded to two places after the decimal point. 14 11
please anyone answer all the questions as soon please 2 4 3 3 4 1. Given three points A = (0,–8, 10), B = (2, -5, 11), C = (-4,-9, 7) in R3. (a) Show that these three points are not collinear (not in a straight line). (b) Find the area of the triangle ABC. (c) Find the scalar equation of the plane containing the points A, B and C. (d) Find a point D on the plane such that...
Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle between v and w. (b) Consider the projection proj, w of w onto v, and then project this projection on u to get proju (proj, w). Is this necessarily equal to the projection proj, w of w on u? Prove or give a counterexample. (c) Find the volume of the parallelepiped with edges formed by u-(2,5,c), v (1,1,1) and w...