Question

If three unit vectors are inclined at an angle of $60^{\circ }$ with each other, then the magnitude of their resultant vector will be

• A. zero
• B. $\sqrt{6}$
• C. $\sqrt{3}$
• D. $\sqrt{9}$

Answer 1

Answer: (B)

We assume $\hat{a}+\hat{b}+\hat{c}=\overrightarrow{R}$
$\overrightarrow{R}\cdot \overrightarrow{R}=\left(\hat{a}+\hat{b}+\hat{c}\right)\cdot \left(\hat{a}+\hat{b}+\hat{c}\right)$
$R^2=1+1+1+cos60+cos60+cos60+cos60+cos60+cos60$
$R^2=6$
$R=\sqrt{6}$