Question

If $\overrightarrow{P}.\overrightarrow{Q}=PQ$ then the angle between $\overrightarrow{P}\text{and}\overrightarrow{Q}$

• A. $\begin{array}{l}0°\end{array}$
• B. $\begin{array}{l}30°\end{array}$
• C. $45°$
• D. $60°$

Answer 1

The correct option is A

$\begin{array}{l}0°\end{array}$

Explanation for the correct option:

Apply the concept of “dot product of two vectors”.

Let two vectors are $\overrightarrow{P}\text{and}\overrightarrow{Q}$then their “dot product ”

$\therefore \overrightarrow{P}.\overrightarrow{Q}=\left|P\right|\left|Q\right|\cos \left(\theta \right)$, where $\theta$ is the angle between vectors $\overrightarrow{P}\text{and}\overrightarrow{Q}$.

$\begin{array}{l}\text{Now,}\overrightarrow{P}.\overrightarrow{Q}=PQ\\ \Rightarrow \left|P\right|\left|Q\right|\cos \left(\theta \right)=PQ\\ \Rightarrow \cos \left(\theta \right)=\frac{PQ}{PQ}\\ \Rightarrow \cos \left(\theta \right)=1\left[\because \cos (0°)=1\right]\\ \Rightarrow \cos \left(\theta \right)=\cos (0°)\end{array}$

Therefore, $\theta =0°$

Hence, the correct option is (A).