Show with the help of a vector diagram that the work done is a scalar product of force and displacement.

Explanation

Suppose that a force `vec(F)` making an angle `theta` with the horizontal is applied on a body which is free to move on a horizontal surface. This force causes a displacement `vec(s)` in the body.

So, work `=(Fcostheta)s=Fcostheta" ...(i)"`
`Fcostheta` is the component of the force in the direction of displacement.
According to definition the scalar product of force `vec(F)` and displacement `vec(s)` is :
`vec(F).vec(s)=Fcostheta " ...(ii)"`
From equation (i) and (ii) we have
`" "W=vec(F).vec(s)`
Thus the scalar product of vectors `vec(F) and vec(s)` gives work which is a scalar quantity.