# Find a plane for four point by WolframAlpha

How can you find the plane of four points by WolframAlpha?

Example

``````plane((0,0,0),(2,-1,-1),(4,-2,-2),(8,-4,-4))
``````

should give me `x + y + z = 0`.

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## migrated from superuser.comDec 26 '10 at 2:07

This question came from our site for computer enthusiasts and power users.

You would have to break it down into pieces and wolfram does not support combined modules like this.

Finding the Vectors

Format : `(2,-1,-1) - (4,-2,-2)`

Finding the Cross Product

Format : `{a1,a2,a3} cross {b1,b2,b3}`

Then substitution of one of the points after that.

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You can do this by querying

plane through (0,0,0),(2,-1,-1),(4,-2,-2),(8,-4,-4)

Note that the points you've written down are all on a line so don't uniquely define a plane. If instead you give it some points which do uniquely define a plane

plane through (0,0,0),(1,0,0),(-1,0,0),(0,1,0)

you get a unique plane as the answer.

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This is one of the things you can't be lazy with using Alpha. Solution: don't be lazy (well, just this once. Spend an hour playing Black Ops to make up for it.)

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