An angle between diagonals
Puzzling Asked on December 16, 2021
The diagonals of a square intersect at a right angle.
Is that true in three dimensions? I.e. would the two diagonals of a cube, each running from one corner of the cube to its opposite corner and crossing in the center, also cross at right angles?
One Answer
There are four diagonals of a cube, but none of them meet at right angles:
To see this, observe that
The two diagonals define a unique plane containing both of them. In that plane, the two cube diagonals are also the diagonals of a rectangle,
Answered by Rand al'Thor on December 16, 2021
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