Question

If the scalar and vector products of two vectors A and B are equal in magnitude, then the angle between the two vectors is

• A. $45°$
• B. $90°$
• C. $180°$
• D. $360°$

Answer 1

The correct option is A

$45°$

Solution:

$$\begin{gathered} |A·B|=|A\times B| \\ \Rightarrow AB\cos \theta =AB\sin \theta \\ \Rightarrow \frac{\sin \theta }{\cos \theta }=\frac{AB}{AB} \\ \Rightarrow \tan \theta =1 \\ \Rightarrow \theta ={\tan }^{-1}\left(1\right) \\ \Rightarrow \theta ={45}^{°} \end{gathered}$$

Hence, the angle between the two vector is ${45}^{°}$.