Question

In the angle subtended by vector $\hat{i}+\hat{j}$ with the x - axis is

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

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

If $\overline{a}=\hat{i}+\hat{j};\overline{b}=\hat{i}$ (x-axis)
then the angle between $\overline{a}$ & $\overline{b}$ is cos $\theta =\frac{\overline{a}.\overline{b}}{|\overline{a}||\overline{b}|}=\frac{(\hat{i}+\hat{j}).\left(\hat{i}\right)}{\sqrt{1^2+1^2}\times \sqrt{1^2}}=\frac{1}{\sqrt{2}}$
$\Rightarrow \theta ={45}^o$