The equation of the line passing through (1,-1,2) and parallel to the line of intersection of the planes  2x−y+z+1=0    and   x−y+z+2=0

The line of intersection of two planes is parallel to the vector which is cross product of two normal vectors  to the plane and it is equal to parallel to the line of intersection of the planes  ijk2−111−11=i(0)−j(1)+k(−1)The direction ratio are proportional to ⟨0,1,1⟩Therefore, the equation of the line passing through the point (1,-1,2) and having direction ratios ⟨0,1,1⟩ is x−10=y+11=z−21