Question

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ have magnitude $3$ each. If $\overrightarrow{A}\times \overrightarrow{B}=-5\hat{k}+2\hat{i}$, then the angle between $A$ and $B$ is

• A. ${\sin }^{-1}\left(\frac{2}{5}\right)$
• B. ${\sin }^{-1}\left(\frac{\sqrt{29}}{9}\right)$
• C. ${\tan }^{-1}\left(\frac{-5}{2}\right)$
• D. ${\cos }^{-1}\left(\frac{\sqrt{29}}{9}\right)$

Answer 1

The correct option is B ${\sin }^{-1}\left(\frac{\sqrt{29}}{9}\right)$

As we know from the cross product $\sin \theta =\frac{|\overrightarrow{A}\times \overrightarrow{B}|}{|\overrightarrow{A}||\overrightarrow{B}|}$
$\Rightarrow \sin \theta =\frac{\sqrt{(-5{)}^2+2^2}}{3\times 3}=\frac{\sqrt{29}}{9}$
$\Rightarrow \theta ={\sin }^{-1}\left(\frac{\sqrt{29}}{9}\right)$