Question

Why work done is a scalar quantity

Answer 1

Work:

It's defined as a dot-product (or scalar product) of force and displacement, both of which are vectors.

A scalar product of two vectors gives a scalar result (aptly named!).

dW=F⃗ ⋅S⃗ =∥F∥∥S∥cosθdW=F→⋅S→=‖F‖‖S‖cos⁡θ
(θθ being the angle between the vectors).

No direction, only magnitude.

A force can do work on a body even displacing at an angle to the direction of force (θθ!).
In other words, work done due to displacement caused by a force is scalar quantity. The dot product of vector quantities is always scalarwhich means it is has only magnitude and no direction.