# Linear Algebra orthogonality problem

1. Apr 11, 2014

### mpittma1

1. The problem statement, all variables and given/known data
Let W be the intersection of the two planes

x + y + z = 0 and x - y + z = 0

In R3. Find an equation for Wτ

2. Relevant equations

3. The attempt at a solution

So, W = {(x, y, z) l 2y =0}

I don't think that is a correct was to represent W being the intersection of the planes though.

I can find Wτ after I know how to find my equation for W.

Any thoughts for how to find the equation for W?

2. Apr 11, 2014

### LCKurtz

$y=0$ alright, but you need more. You also need $x=-z$ for $(x,y,z)$ to be on both planes. Do you see how to write the equation from that?

3. Apr 11, 2014

### mpittma1

Im not seeing how to get x = -z......

4. Apr 11, 2014

### LCKurtz

Look at the equations of the two planes when $y=0$.

5. Apr 11, 2014

### mpittma1

Ok so you "Let" x = -z, so that way when y=0 the equation for the two planes become x + z = 0

so x has to be equal to - z to make -z + z = 0 right?

6. Apr 11, 2014

### LCKurtz

Yes. So what is the equation of the line of intersection?

7. Apr 11, 2014

### mpittma1

x+z = 0?

8. Apr 11, 2014

### LCKurtz

9. Apr 11, 2014

### ythamsten

A tip is to see x=-z as (x-0)/1 = (z-0)/-1.