1. ## vector problem

Describe the shape of the intersection of the plane z=-3 and the plane y=z in three space. I drew out a diagram of z=-3 but im not sure what to do with y=z i know that from what i've learned, every point on y is equal to a point on z and that the x coordinates can be any value.

2. Originally Posted by surffan
Describe the shape of the intersection of the plane z=-3 and the plane y=z in three space. I drew out a diagram of z=-3 but im not sure what to do with y=z i know that from what i've learned, every point on y is equal to a point on z and that the x coordinates can be any value.
Dear surffan,

Since $\displaystyle z=-3~ and~ y=z\Rightarrow{z=y=-3}$

This is a straight line for any x value. Please see the attachement so you will understand this correctly.

3. If you look at just the y-z plane, the equation y=z describes a line. In 3-space, the plane y=z is that same line extended in the positive-x and negative-x direction. You have y=z and x=anything.

The intersection of 2 planes is normally a line. The exceptions are when the two planes are parallel (intersection is empty) or coincident (intersection is a plane).

Ignore the above - Sudharaka's post and picture show it much better. The purple plane going diagonally is the plane y=z, and the pink horizontal plane is z=-3.

4. thank you so much, i couldn't visualize it at all, this is a huge help

5. ## Re: vector problem

Originally Posted by Sudharaka
Dear surffan,

Since $\displaystyle z=-3~ and~ y=z\Rightarrow{z=y=-3}$

This is a straight line for any x value. Please see the attachement so you will understand this correctly.