Question

Which of these is a unit vector that makes an angle of ${60}^{\circ }$ with the positive direction of x axis ?

• A. $-1\hat{i}-\sqrt{3}\hat{j}$
• B. $\frac{-1}{2}\hat{i}-\frac{\sqrt{3}}{2}\hat{j}$
• C. $1\hat{i}+\sqrt{3}\hat{j}$
• D. $\frac{1}{2}\hat{i}+\frac{\sqrt{3}}{2}\hat{j}$

Answer 1

The correct option is D

$\frac{1}{2}\hat{i}+\frac{\sqrt{3}}{2}\hat{j}$

X component - $1cos{60}^{\circ }=1\times \frac{1}{2}=\frac{1}{2}$

Y component - $1sin{60}^{\circ }=1\times \frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2}$

The vector becomes $\frac{1}{2}\hat{i}+\frac{\sqrt{3}}{2}\hat{j}$