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

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

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, $\|\mathbf{u}+\mathbf{v}\|^{2}=\|\mathbf{u}\|^{2}+\|\mathbf{v}\|^{2}$
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