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Q.
If the vectors $a$ and $b$ be such that $| a |=3$ and $| b |=\frac{\sqrt{2}}{3}$, then $a \times b$ is a unit vector , if the angle between $a$ and $b$ is
Vector Algebra
Solution:
It is given that $| a |=3$ and $| b |=\frac{\sqrt{2}}{3}$.
Let $\theta$ be the angle between $a$ and $b$, given $| a \times b |=1$
$\Rightarrow |a||b| \sin \theta=1 $
$\Rightarrow 3 \times \frac{\sqrt{2}}{3} \times \sin \theta=1 $
$\Rightarrow \sin \theta=\frac{1}{\sqrt{2}} \Rightarrow \theta=\frac{\pi}{4}$
Hence, $a \times b$ is a unit vector, if the angle between $a$ and $b$ is $\frac{\pi}{4}$