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I What will be the 4th axis of a 3d curl?

  1. Oct 15, 2016 #1
    Suppose we have do a curl of two 2-d vectors... we get the 3rd axis about which it is rotating. But when we do the curl of two 3-d vectors.. we get a answer like x-y plane is rotating wrt z axis, y-z plane rotating wrt to x axis and similarly x-z plane rotating wrt to y axis.
    My question is, can't we find out the 4th dimension with respect to which all the x-y-z volume is rotating?
  2. jcsd
  3. Oct 15, 2016 #2


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    Staff: Mentor

    Your "two 2-d vectors" and "two 3-d vectors" are actually the exact same thing. The two "3d vectors" lie in a common 2d plane, just as do you "2d" vectors, and then the curl is perpendicular to that plane, in the third dimension.
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