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



should give me x + y + z = 0.


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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