Originally Posted by

**Kakariki** Hey, thanks for coming into my thread!

I have a problem. I am given 3 equations of planes, in the form Ax + By + Cz + D = 0, and am being asked how they are intersecting.

Here are the 3 equations:

1. x + 2y + 3z + 4 = 0

2. x - y - 3z - 2 = 0

3. x + 5y + 9z + 10 = 0

I decided to run it through Gauss Jordan elimination to see if they intersect at the same point:

***I am having trouble working with matrices with latex, so hopefully this makes sense***

Starting with:

1 2 3 -4

1 -2 -3 2

1 5 9 -10

So I subtract line 1 from 2 and line 1 from 3:

1 2 3 -4

0 -3 -6 6 This line is incorrect, it should be 0 -4 -6 6. You will need to recompute everything else from here.

0 3 6 -6

Then I multiply line 1 by 2 and line 2 by -1:

2 4 6 -8

0 3 6 -6

0 3 6 -6

Then I subtract line 2 from line one, and line 2 from line 3 which leaves:

2 1 0 -2

0 3 6 -6

0 0 0 0

I have not encountered this before using this technique. What does it mean? Also, what does it mean with regards to how the planes intersect?

Thank you! Please feel free to ask questions, I will gladly clear anything up that I said here.