Question

If the dot product of two non-zero vectors is zero, then the vectors

• A. are parallel to each other.
• B. are perpendicular to each other.
• C. can have any orientation.
• D. are anti-parallel to each other.

Answer 1

Answer: (B)

are perpendicular to each other.

The scalar product of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is given by.

$\overrightarrow{A}.\overrightarrow{B}=ABcos\theta$

where $\theta$ is the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$

The scalar product will be zero when $\cos \theta$ will be zero.

$\Rightarrow \theta ={90}^{\circ }$, hence, the vectors will be perpendicular to each other.