Question

If vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are such that $\left|\overrightarrow{a}\right|=3$,$\left|\overrightarrow{b}\right|=\frac{\sqrt{2}}{3}$ and $\overrightarrow{a}\times \overrightarrow{b}$ is a unit vector, then find the angle between the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ .

Answer 1

$\overrightarrow{a}\times \overrightarrow{b}=|a||b|\sin \theta$

$1=3\times \frac{\sqrt{2}}{3}\times \sin \theta$

$\sin \theta =\frac{1}{\sqrt{2}}$

$\theta ={45}^{\circ }$