Question

What is dot product geometrically?

Answer 1

Dot product:

By geometrical definition, dot product of two vectors is equal to the product of the magnitude of two vectors and cosine of angle between them.

If $A$ and $B$ are two vectors, then $A.B=\left|A\right|\left|B\right|\cos \left(\theta \right)$ where $\theta$ is the angle between vectors $A$ and $B$.

1. If $\theta =90°$, then $A.B=0$ as $\cos \left(90°\right)=0$$\Rightarrow$the vectors $A$ and $B$ are orthogonal.
2. If $\theta =0°$, then $A.B=\left|A\right|\left|B\right|$ as $\cos \left(0°\right)=1$$\Rightarrow$the vectors $A$ and $B$ are parallel.

Hence, the dot product is explained.