If there is a set for 3D vectors $v$ where
$ v \times \begin{pmatrix} -1 \\ 1 \\ 4 \end{pmatrix} = \begin{pmatrix} 5 \\ -27 \\ 8 \end{pmatrix}$
is a line, what is this line's equation?

I'm not sure how to solve this, except for setting $v = \begin{pmatrix} a \\ b \\ c \end{pmatrix}$ and maybe having a linear system of equations, but I don't see how I could use that to solve the problem.