I know that three planes can intersect having a common straight line as intersection. But I have seen in some references that three planes intersect at single point.The three planes were represented by a triangle. What is equation of a triangle?

Thanks in advance.

  • 4
    $\begingroup$ Really? Are you familiar with $\mathbb R^3$? $\endgroup$
    – John Douma
    Jan 22 at 5:19
  • $\begingroup$ They can be triangularly shaped. $\endgroup$
    – bumblebee
    Jan 22 at 5:19
  • $\begingroup$ Two non-parallel planes intersect in a line. If that line is not parallel to the third plane, then it passes through it at a single point. $\endgroup$
    – Karl
    Jan 22 at 5:45
  • 1
    $\begingroup$ what about the three coordinate planes?? $\endgroup$
    – GReyes
    Jan 22 at 5:47
  • 2
    $\begingroup$ The x-y,y-z and z-x plane intersecting at origin. $\endgroup$ Jan 22 at 5:55

1 Answer 1


The general equation for a plane is $ax+by+cz=d$ for constants $a,b,c,d.$

I can't comment on the specific example you saw; you may often see a triangle as a representation of a portion of a plane in a particular octant. But three planes can certainly intersect at a point: consider the three coordinate planes, $x=0,y=0,z=0$.

enter image description here

And if you want all possibilities: ![enter image description here

  • $\begingroup$ Golden_Ratio. Very nice. $\endgroup$ Jan 22 at 8:07
  • $\begingroup$ Thanks @PeterSzilas $\endgroup$ Jan 22 at 8:13

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