Question

Find the indicated dot product. r = <9, -7, -8>, v = <3, 4, 7>, w = <6, -9, 7> v ⋅ w

Answer 1

v ⋅ w = (3)(6) + (4)(-9) + (7)(7)
v ⋅ w = 18 - 36 + 49
v ⋅ w = 31

The final answer is 31

Answer 2

The indicated dot product of v.w is 31.

Explanation:

Given : r = <9, -7, -8>, v = <3, 4, 7>, w = <6, -9, 7>

To find : The indicated dot product v.w?

Solution :

The dot product in
`R^3` is

If
`v=ai+bj+ck` and
`u=di+ej+fk`

Then,
`v.w=ad+be+cf`

We have given,

v = <3, 4, 7>, w = <6, -9, 7>

where, a=3 ,b=4, c=7 and d=6, e=-9, f=7

So,
`v.w=ad+be+cf`

`v.w=3(6)+4(-9)+7(7)`

`v.w=18-36+49`

`v.w=31`

Therefore, The indicated dot product of v.w is 31.