Question

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

Answer 1

Here, $|\overrightarrow{a}|=3$ and $|\overrightarrow{b}|=\frac{3}{2}$ and $|\overrightarrow{a}\times \overrightarrow{b}|=1$

We know that $\overrightarrow{a}\times \overrightarrow{b}=|\overrightarrow{a}|.|\overrightarrow{b}|sin\theta$

$\Rightarrow 1=3.\frac{2}{3}.sin\theta$

$1=2sin\theta$

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

$\Rightarrow \theta =\frac{\pi }{6}$