Proving Perpendicularity of DB.AC in a Tetrahedron

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In the discussion about proving the perpendicularity of DB to AC in tetrahedron ABCD, a user seeks assistance with the mathematical proof. They express confusion over the relationships between the edges, particularly questioning the validity of the given conditions. Another participant suggests that projecting vertex A onto the plane BCD may help clarify the perpendicular relationships. The conversation highlights the complexity of the geometric relationships in tetrahedrons and the need for careful consideration of the conditions provided. Overall, the discussion emphasizes the importance of understanding geometric projections in solving such problems.
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Could someone please give me a hint on this question?

In the tetrahedron ABCD, AB is perpendicular to DC and AD is perpendicular to BC, prove that DB is perpendicular to AC.

This is what I am stuck on:

DB.AC = (DC+CB).(AD+dc)
=DC.AD +DC.DC+CB.AD+CB.DC
=(CA+AD).AD+d.d+(CA+AB).DC
=CA.AD+AD.AD+d.d+CA.DC+ab.dc
=-c.d+d.d+d.d+-c.(CA+AD)
-c.d+d.d+d.d+c.c+-c.d
=2d.d+c.c-2(c.d)

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Are you sure you wrote down the question correctly? As it stands, I don't think any tetrahedron's going to satisfy your givens. It seems to me that both AB and BC would have to be perpendicular to the plane through ABC; but then AB and BC would parallel, contradicting the fact that they intersect. However, it's 3:45am by me, so I might have missed something.
 
The problem is OK.
If you project the vertex A onto the plane BCD the projected edges of the tetrahedron are also perpendicular. This might help...

ehild
 

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