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 `4m` along the z-axis only,
`S=0hati+0hatj+4hatk`
Also, `F=-i+2hatj+3hatk`
Work done,
`W=vecF.vecS=(-hati+2hatj+3hatk)*(0hati+hatj+4hatk)`
`=12(hatk.hatk)J=12J`