Question
In a tetrahedron, if two pairs of opposite edges are perpendicular, then the third pair is also perpendicular to each other and the sum of the sequares of two opposite edges is the same for each pair.
Solution
Let ABCD be the tetrahedron. Take D as origin,
are position vectors of A, B, C respectively with D as origin. Let DA and CB be perpendicular.
Let DB and AC be perpendicular.
Again,
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are position vectors of A, B, C respectively with D as origin. Let DA and CB be perpendicular.Let DB and AC be perpendicular.
Again,
