A particle is displaced from a position `(2hati - hatj+hatk)` to another position `(3hati+2 hatj -2hatk)` under the action of the force `(2 hati + hatj - hatk)`. The work done by the force in arbitrary unit is 

Options

A. 8
B. 10
C. 12
D. 16

Answer

A

Explanation

Here , `vec(r_1) = 2 hati - hatj + hatk, vec(r_2) = 3hat(i) + 2hat(j) - 2hat(k)`
`vecF = 2 hati + hatj - hatk`
Displacement, `vecr = vec(r_2) - vec(r_1) = (3hati + 2hatj - 2hatk) - (2hati - hatj + hatk)`
`= hati + 3hatj - 3hatk`
`W = vec(F).vec(r) = (2hati + hatj - hatk).(hati + 3hatj - 3hatk) = 2 + 3 + 3 = 8` units