= Solution
Take the <cross product> with $\mathbf c$. Since $\mathbf c\times\mathbf c=0$, the equation implies
$$
\mathbf x\times\mathbf c=\mathbf a\times\mathbf c,
\qquad(\mathbf x-\mathbf a)\times\mathbf c=0.
$$
As $\mathbf c\ne0$, the displacement is parallel to $\mathbf c$. Therefore
$$
\boxed{\mathbf x=\mathbf a+\lambda\mathbf c,\qquad\lambda\in\mathbb R}.
$$
This is a necessary condition; substitution must still determine which points on this <straight line> satisfy the full equation.
Back to article page
