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 $\hat{a}+\hat{b}+\hat{c}=\overset{ \rightarrow }{R}$
$\overset{ \rightarrow }{R}\cdot \overset{ \rightarrow }{R}=\left(\hat{a} + \hat{b} + \hat{c}\right)\cdot \left(\hat{a} + \hat{b} + \hat{c}\right)$
$R^{2}=1+1+1+cos 60+cos ⁡ 60+cos ⁡ 60+cos ⁡ 60+cos ⁡ 60+cos ⁡ 60$
$R^{2}=6$
$R=\sqrt{6}$