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, $-\vec{a}=\vec{b}+\vec{c}$
$\Rightarrow \left|\vec{a}\right|^{2}=\left|\vec{b}\right|^{2}+\left|\vec{c}\right|^{2}+2\left|\vec{b}\right|\left|\vec{c}\right|cos\,\theta$
$=30\,cos\,\theta=15$
$\Rightarrow cos\,\theta=\frac{1}{2}$
$\theta=60^{\circ}$