Hi,(adsbygoogle = window.adsbygoogle || []).push({});

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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Line of intersection of two planes

**Physics Forums | Science Articles, Homework Help, Discussion**