Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2009 / Paper 2 / 11 / b / Solution

The plane normals are $n_1=(2,-1,-1)$ and $n_2=(3,-1,-3)$. Their cross product is $(2,3,1)$, perpendicular to both normals and hence parallel to the intersection line. Setting $z=0$ in both equations gives the common point $(1,-1,0)$. ThereforeThe normals are not parallel, so their intersection is a unique line.