1. In R5, let a (-4, 4, 9, (a) Compute the coordinates of the linear combination

Question

1. In R5, let a (-4, 4, 9, (a) Compute the coordinates of the linear combination 3a -2b -(c-2b+3a) (b) Solve the vector equation below for x; then compute the coordinates of x. 2(x-5a) = 9(c-4b) + x 2. In R' you are given the points (a) Write out all possible arrows which can be formed using the points P.Q. R. (Hint: If your list of arrows is complete, there should be nine of then.) (b) For each of the arrows from part (a), find the vector it represents. (c) Which pairs of vectors from part (b) are parallel? Ile [10 3. (On lincar motions) The linear motions of two particles in R3 are described by u: R- Rs, 11(s) (2.0.0) + s(1.3, 1) (a) Find the location of the u-particle at tune b) Determine at which time (if over) the v-particle passes through 15,-.1

Explanation / Answer

Question 2

a) The 9 set of vectors will be

PQ, PR,QR,(PQ+PR),(PQ-PR),(QP+QR),(QP-QR),(RP+RQ) and (RP-RQ)

b) The vector representation of the arrow will be

PQ = <9,-5,1,3> - <2.2.2.2> = <7,-7,-1,1>

PR = <6,8,-4,1> - <2,2,2,2> = <4,6,-6,-1>

QR = <6,8,-4,1> - <9,-5,1,3> = <-3,13,-5,-2>

PQ + PR = <11,-1,-7,2>

PQ - PR = <3,-13,5,2>

QP + QR = <-10,20,-4,-3>

QP - QR = <-4,-6,6,1>

RP + RQ = <-1,-19,11,3>

RP - RQ = <-7,7,1,-1>

c)

PQ is parallel to RP - RQ

PR is parallel to QP - QR

QR is parallel to PQ - PR

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