Given the vectors u=<2,2>, v=<-3,4>, and w=<1,-2>, how do you find (u*2v)w?

1 Answer
Nov 1, 2016

(vecu*2vecv)vecw = <<4,-8>>

Explanation:

Inner Product Definition
If vecA = <<(a_1, a_2, a_3)>> , and vecB = <<(b_1, b_2, b_3)>> , then the inner product (or dot product), a scaler quantity, is given by:
vecA * vecB = a_1b_1 + a_2b_2 + a_3b_3

Inner Product = 0 hArr vectors are perpendicular

So, vecu=<<2,2>>, and vecv=<<-3,4>>, and vecw=<<1,-2>>

Then;
(vecu*2vecv)vecw = 2(vecu*vecv)vecw
:. (vecu*2vecv)vecw = 2{(2)(-3)+(2)(4)}vecw
:. (vecu*2vecv)vecw = 2(-6+8)vecw
:. (vecu*2vecv)vecw = 2(2)vecw
:. (vecu*2vecv)vecw = 4vecw
:. (vecu*2vecv)vecw = 4<<1,-2>>
:. (vecu*2vecv)vecw = <<4,-8>>