Question

The angle made by the vector $\overrightarrow{A}=\hat{i}+\hat{j}$ with $x-$axis is-

• A. ${90}^o$
• B. ${45}^o$
• C. ${22.5}^o$
• D. ${30}^o$

Answer 1

The correct option is B ${45}^o$

Given $\overrightarrow{A}=\hat{i}+\hat{j}$ $\Rightarrow |\overrightarrow{A}|=\sqrt{2}$,

Let angle is $\theta$

$\Rightarrow \overrightarrow{A}.\hat{i}=|\overrightarrow{A}|cos\theta$

$\Rightarrow (\hat{i}+\hat{j}).\hat{i}=\sqrt{2}cos\theta$ $\Rightarrow cos\theta =\frac{1}{\sqrt{2}}$ $\Rightarrow \theta ={45}^o$