Question

A vector of magnitude $5$ units makes an angle ${120}^o$ with positive x-axis in anti-clockwise direction. The given vector is

• A. $\frac{5}{2}\hat{i}-\frac{\sqrt{3}}{2}\hat{j}$
• B. $\frac{5}{2}\hat{i}+\frac{\sqrt{3}}{2}\hat{j}$
• C. $\frac{-5}{2}\hat{i}-\frac{\sqrt{3}}{2}\hat{j}$
• D. $\frac{-5}{2}\hat{i}+\frac{5\sqrt{3}}{2}\hat{j}$

Answer 1

The correct option is D $\frac{-5}{2}\hat{i}+\frac{5\sqrt{3}}{2}\hat{j}$

Given,

Amplitude $A=5$ and angle $\theta ={120}^o$

$\overrightarrow{V}=A\cos \theta \hat{i}+A\sin \theta \hat{j}$

$\overrightarrow{V}=5\cos {120}^o\hat{i}+5\sin {120}^o\hat{j}$

$\overrightarrow{V}=\frac{-5}{2}\hat{i}+\frac{5\sqrt{3}}{2}\hat{j}$