Question

Find the angle between two vectors $\vec{a}$ and $\vec{b}$ with magnitudes $\sqrt3$ and $2$, respectively having $\vec{a}.\vec{b}=\sqrt{6}.$

Answer 1

The correct answer is:$\frac{π}{4}$
It is given that,
$|\vec{a}|=\sqrt{3},|\vec{b}|=2$ and $\vec{a}.\vec{b}=\sqrt{6}$
Now,we know that $\vec{a}.\vec{b}=|\vec{a}||\vec{b}|cosθ.$
$∴\sqrt{6}=\sqrt3\times2\times cosθ$
$⇒cosθ=\frac{1}{\sqrt2}$
$⇒θ=\frac{π}{4}$
Hence,the angle between the given vectors $\vec{a}$ and $\vec{b}$ is $\frac{π}{4}$.