Question

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two unit vectors if the vectors $\overrightarrow{c}=\overrightarrow{a}+2\overrightarrow{b}$ and $\overrightarrow{d}=2\overrightarrow{a}-4\overrightarrow{b}$ are perpendicular to each other. Then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is:

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

Answer 1

The correct option is C $\frac{\pi }{3}$

dot product of $c.d=0$

$(\overrightarrow{a}+2\overrightarrow{b})(2\overrightarrow{a}-4\overrightarrow{b})=0$

$2a^2-4ba+4ba-8b^2=06ab=3ab=\frac{1}{2}$

Correct answer $C$, $\frac{\pi }{3}$