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How to think of a plane

  1. Oct 29, 2011 #1

    I am trying to solve a problem that involves "the plane y=z". How exactly should I think of this plane? It's obviously one of three planes that can be formed between the three diffirent axes, but which one? What is the intuition behind "y=z"?

    A really basic question to some of you, I bet. Any help would be appreciated. The understanding behind it all is what I really want to achieve (not just the right answer).

  2. jcsd
  3. Oct 30, 2011 #2
    In the y-z plane draw a line of 45 degrees. This line should be the cross section of the plane you want to imagine.
  4. Oct 30, 2011 #3


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    As Anshuman said, first draw a yz-coordinate plane and draw the line y= z (through the origin, at 45 degrees to the axes. Now imagine the x-axis coming out of the paper toward you and the plane being that line coming straight out.
    For example, the plane contains the points (x, a, a) for any x or a.
  5. Oct 30, 2011 #4


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    another way to think of this plane, is that it consists of all vectors of the form:

    x(1,0,0) + y(0,1,1), for any real numbers x,y.

    that is, P = span({(1,0,0), (0,1,1)}).

    this plane intersects the "x-axis" (the line x(1,0,0)) and the line y = z. (if we are looking perpendicular to the x-axis (from the "negative part" where x < 0, so the positive numbers are ahead of us) at the yz-plane, we would see our plane "tilted" 45 degrees to the left. if we were on the "positive side" of the x-axis, perpendicluar to it and looking towards the origin, we would see our plane as titled 45 degrees to the right).

    driving up our plane parallel to the y-axis it's a rather steep grade, but if we make a left or right turn, and go parallel to the x-axis, it's perfectly flat (unless it's icy, in which case we'll slip down it sideways).
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