Question

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are vectors such that$\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$ and $|\overrightarrow{a}|=7,|\overrightarrow{b}|=5,|\overrightarrow{c}|=3$ then the angle between the vectors $\overrightarrow{b}and\overrightarrow{c}$ is

• A. 30${}^{\circ }$
• B. 45${}^{\circ }$
• C. 60${}^{\circ }$
• D. 90${}^{\circ }$

Answer 1

Answer: (C)

Let $\theta$ be the angle between $\vec{b}$ and $\vec{c}$.
Given, $-\vec{a}=\vec{b}+\vec{c}$
$\Rightarrow {\left|\vec{a}\right|}^2={\left|\vec{b}\right|}^2+{\left|\vec{c}\right|}^2+2\left|\vec{b}\right|\left|\vec{c}\right|cos\theta$
$=30cos\theta =15$
$\Rightarrow cos\theta =\frac{1}{2}$
$\theta =60^{\circ }$