Question

Explain the scalar product of two vectors.

Answer 1

Scalar Product of Vectors:

1. The dot product or scalar product of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$, denoted by $\overrightarrow{A}.\overrightarrow{B}$, is defined as the product of the magnitudes of $\overrightarrow{A}$ and $\overrightarrow{B}$ and the cosine of the angle $\theta$ between them.
2. In symbols, $\overrightarrow{A}.\overrightarrow{B}=\left|\overrightarrow{A}\right|\left|\overrightarrow{B}\right|\cos \theta ,$ $0\le \theta \le \mathrm{\pi }$
3. From the name itself, we can understand that the product is a scalar quantity and hence has only magnitude and no direction.