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Homework Help: Surfaces in R3

  1. Jul 3, 2011 #1
    What does a surface in R3 that intersects plane x = y at a line for every value of x represent?

    My first intuition is that it represents a plane because in R3 planes intersect at lines but I feel like there is a counterexample to this.
  2. jcsd
  3. Jul 3, 2011 #2


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    It doesn't need to be s plane.

    The surface z = x2 intersects the plane y = x for every value of x.

    So does x = z3.
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