Question

If a, b are two vectors such that $\left|a\right|=\sqrt{2}$, $\left|b\right|=2$ and $a.b=\sqrt{6}$. Find the angle between a and b.

Answer 1

Given,

$\left|a\right|$ $=$ $\sqrt{2}$ , $\left|b\right|$ $=2$ and $a.b=$$\sqrt{6}$

We know,

$\left|a\right|\left|b\right|\cos \theta$ $=$ $a.b$

($\sqrt{2}$)(2)$\cos \theta$ $=$ $\sqrt{6}$

$\cos \theta$ $=$ $\frac{\sqrt{6}}{2\sqrt{2}}$

$\cos \theta$ $=$ $\frac{\sqrt{3}}{2}$

$\theta$ $=$ $30$

so , angle between a and b is 30 .