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

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Aicharya · Accepted Answer

$\begin{aligned} & \overline{\mathrm{a}}+\overline{\mathrm{b}}=-\overline{\mathrm{c}} \Rightarrow|\overline{\mathrm{a}}+\overline{\mathrm{b}}|^2=|\overline{\mathrm{c}}|^2 \ & 	herefore|\overline{\mathrm{a}}|^2+|\overline{\mathrm{b}}|^2+2|\overline{\mathrm{a}}||\overline{\mathrm{b}}| \cos 	heta=|\overline{\mathrm{c}}|^2 \ & 	herefore(3)^2+(5)^2+2(3)(5) \cos 	heta=(7)^2 \ & 	herefore \cos 	heta=\frac{49-34}{30}=\frac{1}{2} \Rightarrow 	heta=\frac{\pi}{3}\end{aligned}$

If $\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}}=\overline{0}$ with…

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