2017 Specimen Paper P1 Q6

The non-zero vectors \(\mathbf{a}\),\(\mathbf{b}\) and \(\mathbf{c}\) are such that \(\mathbf{a}\times \mathbf{b}=\mathbf{c}\times \mathbf{a}\). Given that \(\mathbf{b}\ne -\mathbf{c}\), find a linear relationship between \(\mathbf{a}\),\(\mathbf{b}\) and \(\mathbf{c}\).[3]

The variable vector \(\mathbf{v}\) satisfies the equation \(\mathbf{v}\times \left( \mathbf{i}-3\mathbf{k} \right)=2\mathbf{j}\). Find the set of vectors \(\mathbf{v}\) and describe this set geometrically.[5]