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Question about planes

  1. Nov 28, 2009 #1
    1. The problem statement, all variables and given/known data

    In R^3, what does the pair of equations y=3 and z=5 represent? In other words, describe the set of points (x,y,z) such that y=3 and z=5.

    3. The attempt at a solution

    I drew out the individual planes y=3 and z=5. i am not sure how to describe the set of all points that satisfy both constraints?

    I have to have the set of all points such that for ALL x-->y=3 and z=5.

    Is that a surface? Or a line? I am thinking it has to be a line?

    thoughts?
     
  2. jcsd
  3. Nov 28, 2009 #2
    It might help to be a little more specific about the planes..

    y = 3 is a plane, and it is parallel to the xz-plane.
    z = 5 is a plane, and it is parallel to the xy-plane.

    So the set of all (x,y,z) such that y=3 and z=5 is given by the intersection of these two planes, and since one is parallel to the xz-plane and the other is parallel to the xy-plane, then the intersection of y=3 and z=5 is a ______
     
  4. Nov 28, 2009 #3
    line!

    Though, I am not sure why it is so important to note that each line is parallel to a coordinate plane? The intersection of 'any' 2 planes is a line, correct? No matter what their orientation is?

    Thanks!
     
  5. Nov 28, 2009 #4
    well.. it's been a while since i've thought about things like that, but yeah, you're right. unless it's a trivial case where the two equations represent the same plane. either way, noting they're parallel to coordinate planes might help you visualize it better, but if you drew a picture anyway, it sounds like you're all set.
     
  6. Nov 28, 2009 #5
    I see. It has been a while for me too, so I am right there with you :smile: Thanks for chiming in xeno_gear!
     
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