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arrow_back Show that $\mathbf{u}=(-2,3,1,4)$ and $\mathbf{v}=(1,2,0,-1)$ are orthogonal

by Platinum
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Show that $\mathbf{u}=(-2,3,1,4)$ and $\mathbf{v}=(1,2,0,-1)$ are orthogonal

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We leave it for you to confirm that $$ \begin{aligned} &\mathbf{u}+\mathbf{v}=(-1,5,1,3) \\ &\|\mathbf{u}+\mathbf{v}\|^{2}=36 \\ &\|\mathbf{u}\|^{2}+\|\mathbf{v}\|^{2}=30+6 \end{aligned} $$ Thus, $\|\mathbf{u}+\mathbf{v}\|^{2}=\|\mathbf{u}\|^{2}+\|\mathbf{v}\|^{2}$
by Platinum
(106,962 points)

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