Question

Two vector $\overrightarrow{A}and\overrightarrow{B}$have magnitude 3 each

$\overrightarrow{A} \times \overrightarrow{B} = - 5\widehat{k} + 2\widehat{i}$. Find angle between A and B.

• A. (a) cos^-1$\frac{\sqrt{29}}{9}$
• A. (b) tan^-1$\left( \frac{- 5}{2} \right)$
• A. (c) sin^-1$\left( \frac{2}{5} \right)$
• A. (d) sin^-1$\left( \frac{\sqrt{29}}{9} \right)$

Answer 1

(d)

sin θ = $\frac{|\overrightarrow{A} \times \overrightarrow{B}|}{|\overrightarrow{A}||\overrightarrow{B}|} = \frac{\sqrt{5^{2} + 2^{2}}}{9}$= $\frac{\sqrt{29}}{9}$ or sin^-1$\left( \frac{\sqrt{29}}{9} \right)$