Question

Let $\overset{ \rightarrow }{a}+\overset{ \rightarrow }{b}+\overset{ \rightarrow }{c}=\overset{ \rightarrow }{0}$ , where $\overset{ \rightarrow }{a},\overset{ \rightarrow }{ \, b}$ and $\overset{ \rightarrow }{c}$ are three non-zero vectors such that the angle between $\overset{ \rightarrow }{a}$ and $\overset{ \rightarrow }{b}$ is $\frac{\pi }{3}$ . If the angle between $\overset{ \rightarrow }{b}$ and $\overset{ \rightarrow }{c}$ is $\frac{\pi }{18}$ , then the angle between $\overset{ \rightarrow }{a}$ and $\overset{ \rightarrow }{c}$ is

• A. $\frac{5 \pi }{18}$
• B. $\frac{11 \pi }{18}$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{6}$

Answer 1

Answer: (A)

From the figure, it is clear that $\overset{ \rightarrow }{a},\overset{ \rightarrow }{ b},\overset{ \rightarrow }{c}$ forms a triangle

$\therefore $ Angle between $\overset{ \rightarrow }{a}\&\overset{ \rightarrow }{c}=\pi -\frac{2 \pi }{3}-\frac{\pi }{18}=\frac{5 \pi }{18}$