# arrow_back Show that if $\mathbf{v}$ is orthogonal to both $\mathbf{w}_{1}$ and $\mathbf{w}_{2}$, then $\mathbf{v}$ is orthogonal to $k_{1} \mathbf{w}_{1}+k_{2} \mathbf{w}_{2}$ for all scalars $k_{1}$ and $k_{2}$.

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Show that if $\mathbf{v}$ is orthogonal to both $\mathbf{w}_{1}$ and $\mathbf{w}_{2}$, then $\mathbf{v}$ is orthogonal to $k_{1} \mathbf{w}_{1}+k_{2} \mathbf{w}_{2}$ for all scalars $k_{1}$ and $k_{2}$.

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