Question

What is the dot product of `<3,4,1 >` and `<5,-1,2 >`?

Answer 1

13

Explanation:

1. Dot product is distributive.
   (e.g. `a*(b+c)=a*b+a*c`)

2. Dot product of 2 vectors that are perpendicular is zero
   (e.g. `hati*hatj=0`)

`(3hati+4hatj+hatk) * (5hati-hatj+2hatk)`

`= (3hati)*(5hati) + (3hati)*(-hatj) + (3hati)*(2hatk)`

`color(white)(s) + (4hatj)*(5hati) + (4hatj)*(-hatj) + (4hatj)*(2hatk)`

`color(white)(s) + (hatk)*(5hati) + (hatk)*(-hatj) + (hatk)*(2hatk)`

`= 15 + 0 + 0`

`color(white)(s) + 0 - 4 + 0`

`color(white)(s) + 0 + 0 + 2`

`= 13`