Question

The angle between two unit-magnitude coplanar vectors P(0.866, 0.500, 0) and Q (0.259, 0.966, 0) will be

• A. $0^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C ${45}^{\circ }$

The two vectors can be rewritten as
$\overline{p}=0.866\hat{i}+0.5\hat{j}+0\hat{k}$
$\overline{q}=0.259\hat{i}+0.966\hat{j}+0\hat{k}$

$\therefore$ cos$\theta$ = $\frac{\overrightarrow{p}.\overrightarrow{q}}{\left|\overrightarrow{p}\right|\left|\overrightarrow{q}\right|}$

=$\frac{0.866\times 0.259+0.5\times 0.966}{1\times 1}$

= 0.707

=$\frac{1}{\sqrt{2}}$

$\theta$ = ${45}^{\circ }$