If \(\vec{a} \times \vec{b} = \vec{c} \times \vec{d}\) and \(\vec{a} \times \vec{c} = \vec{b} \times \vec{d},\) then show that \((\vec{a}-\vec{d})\) is parallel to \((\vec{b}-\vec{c})\), it is being given that \(\vec{a} \neq \vec{d}\) and \(\vec{b} \neq \vec{c}.\)