Linear Algebra orthogonality problem

[mpittma1]

Homework Statement

Let W be the intersection of the two planes

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

In R³. Find an equation for W^τ

Homework Equations

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 W^τ after I know how to find my equation for W.

Any thoughts for how to find the equation for W?

 

[LCKurtz]

Homework Statement

Let W be the intersection of the two planes

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

In R³. Find an equation for W^τ

Homework Equations

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 W^τ after I know how to find my equation for W.

Any thoughts for how to find the equation for W?

$y=0$ 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?

 

[mpittma1]

$y=0$ 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?

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

 

[LCKurtz]

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

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

 

[mpittma1]

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

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?

 

[LCKurtz]

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

 

[mpittma1]

x+z = 0?

 

[LCKurtz]

No. That is the equation of a plane in 3D. You might look, for example, here:

http://www.math.hmc.edu/calculus/tutorials/linesplanesvectors/

 

[ythamsten]

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