Question

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

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{2}$

Answer 1

Answer: (B)

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 $\frac{\pi }{4}$