Work done by a force F on a body is W = F .s, where s is the displacement of body. Given that under a force `F = (2 hat I +3 hat j +4 hat k)` N a body is displaced from position vector `r_1 = (2 hat I +3 hat j + hat k)` m to the position vector `r_2 = (hat i +hat j+ hat k)` m. Find the work done by this force.

Explanation

The body is displacement from `r_(1)"to"r_(2)` . Thereforce , displacemetnt of the body is
`d=r_(2)-r_(1)=(hati+hatj+hatk)-(2hati+3hatj+ hatk)`
`=(-hati-2hatj)m`
Now , work done by the force is
`w=F.d`
`=(2hati+3hatj+4hatk).(-hati-2hatj)`
`=(2)(-1)+(3)(-2)=-8 J`