Let vec{u}, vec{v}, vec{w} be vectors such th | vedclass

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(B) Given that $\vec{u} + \vec{v} + \vec{w} = \vec{0}$.Squaring both sides,we get $|\vec{u} + \vec{v} + \vec{w}|^2 = |\vec{0}|^2$.Using the identity $

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$-25$

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(B) Given that $\vec{u} + \vec{v} + \vec{w} = \vec{0}$.Squaring both sides,we get $|\vec{u} + \vec{v} + \vec{w}|^2 = |\vec{0}|^2$.Using the identity $|\vec{a} + \vec{b} + \vec{c}|^2 = |\vec{a}|^2 + |\vec{b}|^2 + |\vec{c}|^2 + 2(\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a})$,we have:$|\vec{u}|^2 + |\vec{v}|^2 + |\vec{w}|^2 + 2(\vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} + \vec{w} \cdot \vec{u}) = 0$.Substituting the given magnitudes $|\vec{u}| = 3$,$|\vec{v}| = 4$,and $|\vec{w}| = 5$:$3^2 + 4^2 + 5^2 + 2(\vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} + \vec{w} \cdot \vec{u}) = 0$.$9 + 16 + 25 + 2(\vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} + \vec{w} \cdot \vec{u}) = 0$.$50 + 2(\vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} + \vec{w} \cdot \vec{u}) = 0$.$2(\vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} + \vec{w} \cdot \vec{u}) = -50$.Therefore,$\vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} + \vec{w} \cdot \vec{u} = -25$.

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

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