A force `(F) = - 5 hati - 7hatj + 3hatk` acting on a particles causesa displacement `(s) = 3hati - 2hatj + ahatk`n its own direction. If the work done is 14 J, then the vaule of 'a' is

Options

A. 0
B. 5
C. 15
D. 1

Answer

B

Explanation

Given `F = - 5hati - 7 hatj + 3hatk`
`s = 3hati - 2hatj + ahatk`
and W = 14 J
The work done by a force in displacing a particle through a distance is given by .
`W = F.S " "…….(i)`
Substituting above values in Eq. (i) we get
`14 = (-5hati - 7hatj + 3hatk) . (3hati - 2hatj + ahatk)`
`rArr " " 14 =- 15 + 14 + 3a`
`rArr" "a=(15)/(3) = 5` .