My guess is that it is either a bug or a restriction on how RegionEqual[]
works with InfinitePlane[]
.
Here's a way to convert InfinitePlane[]
to an ImplicitRegion[]
, on which RegionEqual[]
works:
RegionEqual[
ImplicitRegion[RegionMember[#, {x, y, z}], {x, y, z}] &@
InfinitePlane[{5/Sqrt[74], -(7/Sqrt[74]), 0},
{{-(5/Sqrt[74]), 1 + 7/Sqrt[74], 0}, {0, 0, 1}}],
ImplicitRegion[RegionMember[#, {x, y, z}], {x, y, z}] &@
InfinitePlane[{0, 1, 0},
{{-(5/Sqrt[74]), 1 + 7/Sqrt[74], 0}, {0, 0, 1}}]
]
(* True *)
Note that RegionEqual
fails on the simplest of equivalent InfinitePlane
regions:
RegionEqual[
InfinitePlane[{-1, 1, 0}, {{1, 0, 0}, {0, 0, 1}}],
InfinitePlane[{0, 1, 0}, {{1, 0, 0}, {0, 0, 1}}]
]
(* False *)