Browse Questions

# If $\overrightarrow a\;and\:\overrightarrow b$ are unit vectors and if vectors $\overrightarrow c=\overrightarrow a+2\overrightarrow b$ and $\overrightarrow d=5\overrightarrow a-4\overrightarrow b$ are $\perp$ to each other, then the angle between $\overrightarrow a\;and\:\overrightarrow b$ is ?

Given: $|\overrightarrow a|=|\overrightarrow b|=1$ and $\overrightarrow c\:and\:\overrightarrow d$ are $\perp$.
$\Rightarrow \overrightarrow c.\overrightarrow d=0$
$\Rightarrow(\overrightarrow a+2\overrightarrow b).(5\overrightarrow a-4\overrightarrow b)=0$
$\Rightarrow\:5|\overrightarrow a|^2-8|\overrightarrow b|^2+6\overrightarrow a.\overrightarrow b=0$
$\Rightarrow\:\overrightarrow a.\overrightarrow b=\large\frac{1}{2}$
Angle between $\overrightarrow a\:and\:\overrightarrow b$ is $cos^{-1}\bigg(\large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow a||\overrightarrow b|}\bigg)$
$=cos^{-1}\large\frac{1}{2}=\frac{\pi}{3}$