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I have:

n = Cross[{-1, 2, 2}, {2, 0, -2}];
p = {1, -1, 1};
plane = ({x, y, z} - p).n == 0 // Expand

Which gives:

10 - 4 x + 2 y - 4 z == 0

I'd like to divide both sides by -2 to get:

-5 + 2x - y + 2z == 0

Easy way?

David
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    -#/2 & /@ plane // Expand. See here, for instance, and linked questions. – march Sep 24 '15 at 04:46
  • Yeah, that's the one I was looking for. – march Sep 24 '15 at 06:12
  • @march Interesting. Your technique work, but I had tried plane/2 // Expand and got 1/2 (10 - 4 x + 2 y - 4 z == 0). Curious as to why? – David Sep 24 '15 at 06:21
  • Arithmetical operations like Plus has the Attribute Listable, which means that it will automatically Map over Lists, but just as most functions, it doesn't automatically Map over anything else. The Head of an equation is Equal (look at the FullForm of your equation), and Plus[Equal[ ... ]] won't evaluate. In general, you have to force whatever function you are applying to the expression to move past the Equal. I don't think this is explained very well, but I'm a little tired. So it goes. – march Sep 24 '15 at 06:24

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