Three vectors $\bar{a}, \bar{b}, \bar{c}$ satisfy the condition $\bar{a}+\bar{b}+\bar{c}=\overline{0}$. If $|\bar{a}|=1,|\bar{b}|=3,|\bar{c}|=4$ then $\bar{a} \cdot \bar{b}+\bar{b} \cdot \bar{c}+\bar{c} \cdot \bar{a}=$

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Aicharya · Accepted Answer

$(\vec{a}+\vec{b}+\vec{c})^2=|\vec{a}|^2+|\vec{b}|^2+|\vec{c}|^2+2(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a})$ $\begin{aligned} & 0=(1)^2+(3)^2+(4)^2+2(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}) \ & 2(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a})=-26 \ & \vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}=-13\end{aligned}$

Three vectors $\bar{a}, \bar{b}, \bar{c}$ satisfy the condition $\bar{a}+\bar{b}+\bar{c}=\overline{0}$. If…

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