Why work is a scalar quantity?
If Work=Force×displacement and displacement is a vector quantity so why Work is a scalar quantity
Work is 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.
Thinking logically, what would be the direction of work, anyway? You may say, “In the direction of displacement!”, but then why not in the direction of force? And if you say the direction of both, well then, it isn’t always the same! A force can do work on a body even displacing at an angle to the direction of force (θ!).
=>Note that when θ is 90∘, the result will be zero (cos90∘=0). When force and displacement are perpendicular, the force does no work on the body!