# Thread: Plane parallel to the plane x0y?

1. ## Plane parallel to the plane x0y?

I am working with some vectors but I am failing at understanding and what they mean when they tell me to find a plane parallel to plane x0y? What is this x0y plane? Also I have other questions relation to a plane parallel to 0x, and another one to 0z, how do these planes look like?

2. Originally Posted by Bman900
I am working with some vectors but I am failing at understanding and what they mean when they tell me to find a plane parallel to plane x0y? What is this x0y plane? Also I have other questions relation to a plane parallel to 0x, and another one to 0z, how do these planes look like?
Dear Bman900,

The XOY plane is the plane spanned by the x and y coordinates in the cartesian coordinate system. This is also refered as the xy plane. The "O" represents the origin. Refer, Cartesian coordinate system - Wikipedia, the free encyclopedia for a more detailed discription about the cartesian coordinate system.

3. Oh I think I get it now, but for 0x wouldn't a plane span across the y cordinate as well since x and y are co planar?

4. Originally Posted by Bman900
I am working with some vectors but I am failing at understanding and what they mean when they tell me to find a plane parallel to plane x0y? What is this x0y plane? Also I have other questions relation to a plane parallel to 0x, and another one to 0z, how do these planes look like?
I'm guessing ...

Since you mentioned a 0x-plane and a 0y-plane I assume that x0y-plane is referring to a plane with the equation
$x+y=0$ or more generally to a plane with the equation $ax + by =0$.

I've attached a sketch of a "x0y-plane" (?)

EDIT: As I've learned now my guess was wrong.

5. Originally Posted by Bman900
Oh I think I get it now, but for 0x wouldn't a plane span across the y cordinate as well since x and y are co planar?
OX, OY and OZ are lines. Therefore there are many planes parallel to them. But does you question states "ox plane", "oz plane" etc?

6. Yes, here is an example of a question: Write the equation of a plane which is parallel to the plane 0x and passes through M(4,0,-2) and M(5,1,7).
Now I know how to solve these when there is a regular vector and point but since I can't imagine this 0x, 0z, plane, its hard for me to get started.

I don't know if this would make it clearer but in a previous excersise when he had the question: Write the equation of a plane which is parallel to the plane x0y and crosses through M(2,5,3). We basicly used the z cordinate vector(0,0,1) to be perpendicular to the plane we were trying to find.

7. Originally Posted by Bman900
Yes, here is an example of a question: Write the equation of a plane which is parallel to the plane 0x and passes through M(4,0,-2) and M(5,1,7).
Now I know how to solve these when there is a regular vector and point but since I can't imagine this 0x, 0z, plane, its hard for me to get started.

I don't know if this would make it clearer but in a previous excersise when he had the question: Write the equation of a plane which is parallel to the plane x0y and crosses through M(2,5,3). We basicly used the z cordinate vector(0,0,1) to be perpendicular to the plane we were trying to find.
OX is a line. Therefore it should be "Write the equation of a plane which is parallel to the line 0X and passes through M(4,0,-2) and M(5,1,7)."

Let, $M\equiv (4,0,-2)~and~N\equiv (5,1,7)$

Find the vector $\overline{MN}$. Since the plane is parallel to OX, $\overline{MN}\times i$ gives a perpendicular vector to the plane. Hope you can continue.

8. Thank you for the help, I am understanding this much better!!