Question

100 POINTS! MUST HAVE CORRECT ANSWER AND EXPLAIN YOUR WORK!

Evaluate the expression:

v ⋅ w

Given the vectors:

r = <5, -5, -2>; v = <2, -8, -8>; w = <-2, 6, -5>

(It's an essay question so please explain throughly.)

Answer 1

-12

Explanation:

we have to find the dot product here.

From the formula of dot product of vectors,

we know-

if X=<a,b,c> and Y=<d,e,f>

Then dot product of X and Y is-

X.Y=ad+be+cf

Here, we get

v=<2 , -8 , -8>

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

So, the dot product is-

v . w=2(-2)+(-8)(6)+(-8)(-5)

=-4-48+40

=-52+40

=-12

So,

v . w= -12

Answer 2

Explanation:

we have to find the dot product here.

From the formula of dot product of vectors,

we know-

if X=<a,b,c> and Y=<d,e,f>

Then dot product of X and Y is-

X.Y=ad+be+cf

Here, we get

v=<2 , -8 , -8>

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

So, the dot product is-

v . w=2(-2)+(-8)(6)+(-8)(-5)

=-4-48+40

=-52+40

=-12

So,

v . w= -12