Find Vectors and Perform Vector Operations in R³ Let a = (0, – 5, 5) and 6 = (4, 2, — 5). Find – 2ā + 27. - 2a + 25 =

1. Let x = i +4j + 2k and y = i-3j - k. In this question, write all vectors in i, j, k notation. (a) ( Find |x||. (b) M Find 2x + 3y. (c) Find x. y. (d) Find x × y. Answer: Answer: Answer:

Write the vector as a linear combination.   PQ where P=(3,6) Q=(1,-3)

For the vectors a = <2, 8> and b = <4, 6>    find orthab.

use vectors

Find the sum and difference of the following vectors:     a. <-4,6>+<5,0> b. <-7,5>0<-5,-9>

Find the image of the vector = (1, 2) by rotating it 30° counter-clockwise and scaling it by a factor of 4. Select all answers that are correct. O 2sqrt(3)-4 is the first component O 2+4sqrt(3) is the second component O 2sqrt(3)-4 is the second component O 2+4sqrt(3) is the first component none of these above

Find the vectors T, N, and B at the given point. = (²2², ²²3³, c), (₁, - ²/₁, -1) -3, T = N = B = r(t)

3 -i Rewrite the vector v = in the form a + ib, where vectors a and b have only real components. 4 V2