Question

# Why work is scalar quantity ? In formula it uses force which is vector quantity and displacement which is a part of vector quantity, then why work is scalar quantity ?

Solution

## Dot Product of two vectors a · b is calculated as the following: a · b = |a| × |b| × cos θ Where:|a| is the magnitude (length) of vector a |b| is the magnitude (length) of vector b , θ is the angle between a and b So we multiply the length of a times the length of b, then multiply by the cosine of the angle between a and b we get the magnitude of the work done but not the direction. As there no direction we say that the work is a scalar quantity.

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