A body constrained to move along the z-axis of a co-ordinate system, is subjected to a constant force `vec(F)` given by `vec(F)=-hat(i)+2hat(j)+3hat(k)` Newton where `hat(i),hat(j)`and `hat(k)` represent unit vectors along x-,y-,and z-axes of the system, respectively. Calculate the work done by this force in displacing the body through a distance of `4m` along the z-axis.

Explanation

Since the body is displaced 4 m along z-axis only.
`therefore vecS=0hat(i)+0hat(j)+4hat(k)`
Also `vecF= -hat(i)+2hat(j)+3hat(k)`
Work done, `W=vecF.vecS`
`=(-hat(i)+2hat(j)+3hat(k))`
`=12(veck.veck)` Joule = 12 Joule.