6. Displacement vectors 7 , ū, V, and ū are given below. In the appropriate diagram,...
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...
It is given that the vectors ū = [11,0, 6] and ✓ = (-2,0,–27) lie in a linear subspace W of R'. It follows that, also ū = 29, 0, -36) lies in W. This can be seen by writing was a linear combination of ū and V. Determine the numbers x and y so û = x ·ū+y. V. Give your answer in the form x = a 1y=b for two numbers a and b.
1. Given the vectors ū=(1,-2,-6) and v = (0,-3,4), a) Find u 6v. b) Find a unit vector in the opposite direction to ū. c) Find (ü.v)v. d) Find 11: e) Find the distance between ū and v. f) Are ū and y parallel, perpendicular, or neither? Explain. g) Verify the Triangle Inequality for ū and ū.
6. Are vectors ū= (1,-1,2 %; v = (-1,-1,-1) and W = (-1,-5,1 ) linearly dependent? If they are, write ü as a linear combination of vectors v and w.
Please help solve this while providing a detailed solution = Given vectors ū = (-9, -1, -6]T, ū [10, 2, 7]T E R3. Determine whether the vector [7,-1,4]T is in span{ū, v}. If the vector is in the span then express it as a linear combination of ū, ū. 7 - .
5. Let ū and w be vectors in R3. Prove that (ö - w) x (v + 2) = 2(vx w).
Problem 2 (12 points, 6 for each part) (a) I'm thinking of two vectors ū and ū in R2 such that the standard unit vectors ē; can be expressed as ēj = i + 3ū and ēz = i + 50. Explain, preferably without computing my vectors ū and v, why they span R2. (b) Compute the ū and from part (a).
The displacement vectors A and B shown in the figure above both have magnitudes of 6.00 m. The direction of vector A is 0 = 25.09. a. Give the Cartesian coordinates of both vectors. Calculate the polar coordinates of: b. A - B c. A + B d.ShowĀ + BandĀ – 2B onadiagram. e. There are two vectors, Ū = -2î + 5 and V = -6i - kj where k is some number. The magnitude of is twice as...
1. We are given the following vectors: ū = (x,0,4), ū = (2,1,1) a) What does the value of x need to be so that the vectors ū and ū are perpendicular? Explain your reasoning. (5 pts.) b) Calculate the cross product p = ū xū and find the magnitude of p. (5 pts.) c) Calculate the cross product q = ū xū and find the magnitude of q: (5 pts.) d) Compare the magnitude of p with the magnitude...
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