Question

let the vector $\overrightarrow{a}$ and $\overrightarrow{b}$ be such that $|\overrightarrow{a}|=3$ and $|\overrightarrow{b}|=\frac{\sqrt{2}}{3}$ then $\overrightarrow{a}\times \overrightarrow{b}$ is a unit vector if angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is

• A. $\pi /6$
• B. $\pi /4$
• C. $\pi /3$
• D. $\pi /2$

Answer 1

Answer: (B)

$\pi /4$

$|\overline{a}\times b|=|a||b|since$

$1=3\times \frac{\sqrt{2}}{3}\times sin\theta \Rightarrow sin\theta =\frac{1}{\sqrt{2}}\Rightarrow \theta =\frac{\pi }{4}$

Correct answer is (B)