Consider non-zero vectors \(\mathbf{a}\), \(\mathbf{b}\) and \(\mathbf{c}\) in three-dimensional space.
The non-zero vector \(\mathbf{v}\) is defined as \(\mathbf{v}=(\mathbf{a}\cdot\mathbf{c})\mathbf{b}-(\mathbf{a}\cdot\mathbf{b})\mathbf{c}\).
Show that \(\mathbf{v}\cdot\mathbf{a}=0\).[2]
It is given that \(\mathbf{b}\times\mathbf{c}\) and \(\mathbf{a}\times(\mathbf{b}\times\mathbf{c})\) are non-zero vectors.
Justify why \(\mathbf{b}\cdot(\mathbf{b}\times\mathbf{c})=0\).
Show that \(\mathbf{v}\cdot(\mathbf{b}\times\mathbf{c})=0\).[4]
Hence, state the geometrical relationship between \(\mathbf{v}\) and \(\mathbf{a}\times(\mathbf{b}\times\mathbf{c})\), briefly justifying your answer.[2]