Hi, I was doing a L.A question and a question arose. ( well I will write the question now, I found the answer I just can't visualize what I am doing which bothers me greatly) Find the equation of the plane that contains the line (x,y,z)=(1,0,0)+t(1,3,2), and is parallel to the line of intersection of the two planes -x+2y+z=0 and x+z+1=0 Here is what bothers me: my partner found the answer by putting plane 1 and 2 in an augmented matrix and solving for it ( I'm guessing finding the parametric form). I just found the cross product of the two normals of the planes to find a line parallel to the plane that we are looking for. How can 1) the augmented matrix find a line of intersection ( sorry if the question is broad I can't even understand the concept around that very well) and 2) How can a cross product define a line of intersection? Is there any proof to that? -- again sorry if the questions are hard ot understand / broad. Thank you for your help!