Question

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are such that $|\overrightarrow{A}\times \overrightarrow{B}|=|\overrightarrow{A}.\overrightarrow{B}|$ then the angle between the two vectors is:

• A. $60{}^{\circ }$
• B. $90{}^{\circ }$
• C. $0{}^{\circ }$
• D. $45{}^{\circ }$
• E. $30{}^{\circ }$

Answer 1

Answer: (D)

$|\overrightarrow{A}\times \overrightarrow{B}|=|\overrightarrow{A}.\overrightarrow{B}|$
$\Rightarrow$ $AB\sin \theta \hat{n}=AB\cos \theta \hat{n}$
$\Rightarrow$ $\tan \theta =1$
$\Rightarrow$ $\theta =45{}^{\circ }$