Question

Why do we do Dot Product?

Answer 1

Dot product:

1. Dot product tells us how much a vector applies to another vector.
2. A force vector acting on a position vector is the best example it yields the work done by the vector.
3. Dot product also helps in finding the angle between two vectors using the formula $\cos \theta =\frac{\overrightarrow{a}.\overrightarrow{b}}{\left|a\right|\left|b\right|}$.
4. It is also useful in many applications such as projections, orthogonalization, etc.

Hence, the dot product is very useful for the above reasons.