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  1. #1
    Junior Member surffan's Avatar
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    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.
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  2. #2
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    Quote Originally Posted by surffan View Post
    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 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.

    Hope this will help you.
    Attached Thumbnails Attached Thumbnails vector problem-sp1.png  
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  3. #3
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    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.
    Last edited by hollywood; March 14th 2010 at 05:09 PM. Reason: Previous post answers question
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  4. #4
    Junior Member surffan's Avatar
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    thank you so much, i couldn't visualize it at all, this is a huge help
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  5. #5
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    Re: vector problem

    Quote Originally Posted by Sudharaka View Post
    Dear surffan,

    Since 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.

    Hope this will help you.

    Hi Sudharaka,

    That's a great 3D simulation of the problem! What program did you use to achieve this? Can this be used on a Mac?

    Sheila
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