An engine exerts a force `F=(20hati-3hatj+5hatk)` N and moves with velocity `v=(6hati+20hatj-3hatk) ms^(-1)`. The power of the engine (in watt) is

Options

A. 45 W
B. 10 W
C. 75 W
D. 20 W

Answer

A

Explanation

The power of the engine is given by
`P = vec F cdot vec v`
`=(20 hati -3hatj +5hatk) cdot (6hati +20 hatj -3hatk)`
`=(20xx6)(hati cdot hati) + (-3xx20) (hatj cdot hatj) + (5xx-3) hatk cdot hatk`
`=120 + (-60) +(-15)`
`therefore P =45 W`