Although force vector F and displacement vector S are vector quantities, even then work done W is a scalar quantity, why?

Question

Although force \(\overset{\rightarrow}F\) and displacement \(\overset{\rightarrow}S\) are vector quantities, even then work done W is a scalar quantity, why? If \(\overset{\rightarrow}F\) and \(\overset{\rightarrow}S\) both are non zero, even then W can be zero, when?

Answer 1

Scalar product of force (\(\overset{\rightarrow}F\)) and displacement (\(\overset{\rightarrow}S\)) provides the work done (W); this is why W is a scalar quantity.

If angle between \(\overset{\rightarrow}F\) and \(\overset{\rightarrow}S\) is 90°, then

W = \(\overset{\rightarrow}F.\overset{\rightarrow}S = F.S\cos\ 90^\circ = 0\)