In vector form, work done W is written as:

1. $\vec{W} = \vec{F}.\vec{S}$
2. ${W} = \vec{F}.\vec{S}$
3. ${W} = \vec{F}$x $\vec{S}$cos θ
4. $\vec{W}$= F x S cos θ

${W} = \vec{F}.\vec{S}$

Reason — As force F and displacement S are vector quantities and work W is a scalar quantity so work is expressed as a dot product of force and displacement vectors. Hence, we get the expression : ${W} = \vec{F}.\vec{S}$

The dot product of two vectors is a scalar.