Question

Angle (in rad) made by the vector $\sqrt{3}\hat{i}+\hat{j}$ with the $x$-axis:

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{2}$

Answer 1

Answer: (A)

. $\frac{\pi }{6}$.

$\text{Step 1: Method for finding angle of a vector with x and y axes}$

Let $\overrightarrow{A}=A_x\hat{i}+A_y\hat{j}$

From Figure, In triangle OAB, Angle with x axis is given by:

$tan{\theta }_x=\frac{A_y}{A_x}$

Similarly, In triangle OAC, Angle with y axis is given by:

$tan{\theta }_y=\frac{A_x}{A_y}$

$\text{Step 2: Calculations}$

Given, $\overrightarrow{A}=\sqrt{3}\hat{i}+\hat{j}$

So, Angle with x axis:

$tan{\theta }_x=\frac{A_y}{A_x}=\frac{1}{\sqrt{3}}$

$\Rightarrow {\theta }_x=\frac{\pi }{6}$

Hence correct answer is Option A