Evaluate each expression?

Question

For all problems let s=<-3,1>, u=<4,2>, v=<1,-2>, w=<-2,5>

(a) u * v

(b) (2w) * u

(c) v * (w - s)

Answer 1

Assuming that these are vectors:-
s = - 3 i + j
u = 4 i + 2 j
v = i - 2 j
w = - 2 i + 5 j

Question (a)
u • v = ( 4 i + 2 j ) • ( i - 2 j ) = 4 - 4 = 0

Question (b)
2 (- 2 i + 5 j ) • ( 4 i + 2 j )
(2) ( - 8 + 10 )
4

Question (c)
( i - 2 j ) • ( i + 4 j )
1 - 8
- 7

Answer 2

(a)u.v=4-4=0
(b)2w.u=-16+20=4
(c)V.(w-s)=(1,-2).(1,4)=-7