If $|\bar{a}|=3,|\bar{b}|=5$ and $|\bar{c}|=7$ and $\bar{a}+\bar{b}+\bar{c}=\overline{0}$, then the angle between $\bar{a}$ and $\bar{b}$ is

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Aicharya · Accepted Answer

$\begin{aligned} & \vec{a}+\vec{b}+\vec{c}=0 \ & \Rightarrow \vec{a}+\vec{b}=-\vec{c} \ & \Rightarrow|\vec{a}+\vec{b}|^2=|\vec{c}|^2 \ & \Rightarrow|\vec{a}|^2+|\vec{b}|^2+2|\vec{a}||\vec{b}| \cos 	heta=|\vec{c}|^2 \ & \Rightarrow 3^2+5^2+2 	imes 3 	imes 5 \cos 	heta=7^2 \ & \Rightarrow \cos 	heta=\frac{15}{30}=\frac{1}{2}=\cos \frac{\pi}{3} \ & \Rightarrow 	heta=\frac{\pi}{3}\end{aligned}$

If $|\bar{a}|=3,|\bar{b}|=5$ and $|\bar{c}|=7$ and $\bar{a}+\bar{b}+\bar{c}=\overline{0}$, then the angle…

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