Question

Evaluate the expression: v ⋅ w

Given the vectors:
r = <5, -5, -2>;
v = <2, -8, -8>;
w = <-2, 6, -5>

Answer 1

v ⋅ w = <2, -8, -8> ⋅ <-2, 6, -5> = 2(-2) + -8(6) + -8(-5) = -4 + -48 + 40 = -12

v ⋅ w = -12

Answer 2

Value of v.w equals:

-12

Explanation:

If we are given two vectors a and b as:

a=<x1,x2,x3> and b=<y1,y2,y3>

Then, a.b equals:

a.b=x1y1+x2y2+x3y3

Here, v = <2, -8, -8>

and w = <-2, 6, -5>

v.w= 2×(-2)+(-8)×6+(-8)×(-5)

= -4-48+40

= -4-8

= -12

Hence, Value of v.w equals:

-12