Question

why is work a scalar quantity ??

Answer 1

Simply work is a dot product of force and displacement.It has no direction.
As w=F.ds
w=Fds cosФ,Ф is angle b/w force and displacement.

Answer 2

Work(W)= Force (F) * displacement (s)
W=Fs
Work is a scalar quantity, as it doesn't have any direction but only possesses magnitude. Also, according to a mathematical property, the product of 2 vectors (here force and displacement) is always scalar. VECTOR- A quantity with both, magnitude and direction.
Example: If we push a stone, we apply a force to do so and we say that we apply force to the east (e.g.) and if there is a displacement produced, then we say, it is produced in the eastern direction. But, on the other hand, we never say that work is done towards the east.