No, this is only true if that hyperplane contains the origin; imagine an infinite number of hyperplanes that contain A and B; there are an infinite number of such planes for dimensions higher than 2. Now imagine the same, but connecting O and C; most of those AB hyperplanes are not orthogonal to those OC hyperplanes, it’s only coincidence if they are, though for dimensions higher than 2 you can always find a point C that happens to lie along the orthogonal line from the AB plane to the origin.
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