Question

The rectangular components of a vector are $(2,2)$. The corresponding rectangular components of another vector are $(1,\sqrt{3})$ . Find the angle between the two vectors (in degree).

Answer 1

Let
$\overrightarrow{A}=2\hat{i}+2\hat{j},\overrightarrow{B}=\hat{i}+\sqrt{3}\hat{j}$
$\theta$ be the angle between $\overrightarrow{A}$ & $\overrightarrow{B}$
$\cos \theta =\frac{\overrightarrow{A}.\overrightarrow{B}}{\left|A\right|\left|B\right|}=\frac{2+2\sqrt{3}}{\sqrt{8}.2}$
$\cos \theta =\frac{\sqrt{3}+1}{2\sqrt{2}}$
$\theta ={15}^{\circ }$