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Wait — reconsider: **There is always a unique solution up to addition of a multiple of \(\mathbf{a}\)** to the cross product, but the equation must be consistent with \(\mathbf{v} imes \mathbf{a} \perp \mathbf{a}\).
Since \(egin{pmatrix} 0 \ 0 \ 5 \end{pmatrix}
ot\perp egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}\), **no such vector \(\mathbf{v}\) exists**.

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