Question 8
In the 3-dimensional Euclidean space with origin $O$ and three mutually perpendicular $x$-, $y$- and $z$-axes, two planes $x+y+3z=4$ and $2x-z=6$ intersect at the line $$\mathbf r\times\begin{pmatrix}-1\\a\\b\end{pmatrix}=\begin{pmatrix}-2\\c\\d\end{pmatrix}.$$ Find the value of $|a+b+c+d|$.