Thread: Line of intersection of two planes

2x+3y-5z=0
3x-y+2z=0

I have found the direction vector using the vector product. The answer in the book says the lines goes through point (2,1,1). I think the 0's are a misprint. How do I find that the line goes though that point?

Originally Posted by Stuck Man

2x+3y-5z=0
3x-y+2z=0
I have found the direction vector using the vector product. The answer in the book says the lines goes through point (2,1,1). I think the 0's are a misprint. How do I find that the line goes though that point?

That is indeed a misprint. The line must be a subset of both planes. That point is on neither plane.
The obvious point to pick is .

Is it possible to figure out what the constants should be?

Originally Posted by Stuck Man

Is it possible to figure out what the constants should be?

I have no idea what "the constants should be" could mean.
The line is

The zeroes. If I put the point (2,1,1) into the plane equations I get -4 for the first constant and 7 for the other.

Originally Posted by Stuck Man

The zeroes. If I put the point (2,1,1) into the plane equations I get -4 <-- that should be 2
for the first constant and 7 for the other.

The planes and have the line of interception

With you'll get the point

Yes, thanks.