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Show that there are no vectors u and $\mathbf{v}$ such that $\|\mathbf{u}\|=1$ $\|\mathbf{v}\|=2,$ and $\mathbf{u} \cdot \mathbf{v}=3$...

Question

Show that there are no vectors u and $\mathbf{v}$ such that $\|\mathbf{u}\|=1$ $\|\mathbf{v}\|=2,$ and $\mathbf{u} \cdot \mathbf{v}=3$

Show that there are no vectors u and $\mathbf{v}$ such that $\|\mathbf{u}\|=1$ $\|\mathbf{v}\|=2,$ and $\mathbf{u} \cdot \mathbf{v}=3$



Answers

Show that $\mathbf{v} \times \mathbf{u}$ is orthogonal to $(\mathbf{u} \cdot \mathbf{v})(\mathbf{u}+\mathbf{v})+\mathbf{u},$ where $\mathbf{u}$ and $\mathbf{v}$ are nonzero vectors.


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