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Is there any reason why an InfinitePlane needs a point and two vectors? One would be sufficient. (The one perpendicular to the plane)

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    $\begingroup$ Because in more than three dimensions, a normal and a point do not uniquely determine a plane. $\endgroup$ May 18, 2020 at 10:54
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    $\begingroup$ As noted in the answer below, you can use Hyperplane if you have a normal vector n and point p. An equivalent form would be InfinitePlane[p, NullSpace[{n}]]. $\endgroup$
    – Greg Hurst
    May 18, 2020 at 13:36
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    $\begingroup$ Possible duplicate of How can I create a plane using a point and normal vector? $\endgroup$
    – Jason B.
    May 18, 2020 at 14:16

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You can think about it like this: If you have only one vector, you can rotate the plane around this vector and it would still be valid. Your point would lie on the plane and the vector would point along the plane. You would get infinitely many planes that match this description.

Please see here for more details.

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  • $\begingroup$ Since the plane is infinite, orientation doesn't matter, they will all be the same plane regardless of how you turn it about the axis, I think. Also, consider Hyperplane which works the way OP suggested. You could say the same about the hyperplane, so why does this work for Hyperplane and not for InfinitePlane? $\endgroup$
    – C. E.
    May 18, 2020 at 10:48
  • $\begingroup$ In $n$ dimensions, Hyperplane[] is $n-1$ dimensional, but InfinitePlane[] is always two-dimensional. It is a fortuitous coincidence that these two concepts are equivalent when $n=3$. $\endgroup$ May 18, 2020 at 10:56
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    $\begingroup$ @J.M. Exactly, they are equivalent for $n = 3$. That is what I was hoping to confirm. Consequently, WRI could have supported the point + normal syntax for InfinitePlane, as they did for Hyperplane, if they wanted to, they just chose not to. $\endgroup$
    – C. E.
    May 18, 2020 at 11:31
  • $\begingroup$ Allright, I now take the cross product of my perpendicular vector with {1,0,0} and {0,1,0} and my school geometry tells me that this should work. $\endgroup$
    – Hans W
    May 18, 2020 at 11:34
  • $\begingroup$ @C. E., I agree that it was a deliberate choice to keep the concepts separate. $\endgroup$ May 18, 2020 at 11:49

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