Let $\vec{u}, \vec{v}$ and $\vec{w}$ be vectors such that $|\vec{u}+\vec{v}+\vec{w}=\overline{0}|$. If $|\vec{u}|=3$, $\overrightarrow{|v|}=4$ and $\overrightarrow{|w|}=5$, then the value of $|\vec{u} \cdot \vec{v}+\vec{v} \cdot \vec{w}+\vec{w} \cdot \vec{u}|$ is

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Aicharya · Accepted Answer

$\begin{aligned} & |\vec{u}+\vec{v}+\vec{w}|^2=|\vec{u}|^2+|\vec{v}|^2+|\vec{w}|^2+2(\vec{u} \cdot \vec{v}+\vec{v} \cdot \vec{w}+\vec{w} \cdot \vec{u}) \ & \Rightarrow 0^2=3^2+4^2+5^2+2(\vec{u} \cdot \vec{v}+\vec{v} \cdot \vec{w}+\vec{w} \cdot \vec{u}) \ & \Rightarrow \vec{u} \cdot \vec{v}+\vec{v} \cdot \vec{w}+\vec{w} \cdot \vec{u}=-25\end{aligned}$

Let $\vec{u}, \vec{v}$ and $\vec{w}$ be vectors such that $|\vec{u}+\vec{v}+\vec{w}=\overline{0}|$. If…

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