If (\overrightarrow{a}) and (\overrightarrow{b\_1}) are two... | Mathematics | SolveeIt | Solveeit

Today, August 18

Question

If $\overrightarrow{a}$ and $\overrightarrow{b_1}$ are two unit vectors such that $\overrightarrow{a}+2\overrightarrow{b}$ and $5\overrightarrow{a}-4\overrightarrow{b}$ b, are perpendicular to each other, then the angle between $\overrightarrow{a} and \overrightarrow{b}$ is

A

$45^\circ$

B

$60^\circ$

C

$cos^{-1}\Bigg(\frac{1}{3}\Bigg)$

D

$cos^{-1}\Bigg(\frac{2}{7}\Bigg)$

Answer

$60^\circ$

Explanation

Solution

Since, $(\overrightarrow{a}+2\overrightarrow{b}).(5\overrightarrow{a}-4\overrightarrow{a})=0$
$\Rightarrow \hspace25mm 5|\overrightarrow{a}|^2+6\overrightarrow{a}.\overrightarrow{b}-8|\overrightarrow{b}|^2=0$
$\Rightarrow \hspace35mm 6\overrightarrow{a}.\overrightarrow{b}=3 [\because |\overrightarrow{a}|=|\overrightarrow{b}|=1]$
$\Rightarrow \hspace35mm \cos\theta =\frac{1}{2}\Rightarrow \theta=60^\circ$