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Math Help - Plane parallel to the plane x0y?

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    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?
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    Quote Originally Posted by Bman900 View Post
    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.
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  3. #3
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    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?
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    Quote Originally Posted by Bman900 View Post
    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.
    Attached Thumbnails Attached Thumbnails Plane parallel to the plane x0y?-x0yebene.png  
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    Quote Originally Posted by Bman900 View Post
    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?
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    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.
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    Quote Originally Posted by Bman900 View Post
    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.
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  8. #8
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    Thank you for the help, I am understanding this much better!!
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