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Prove that in a tetrahedron if two pa...

Prove that in a tetrahedron if two pairs of opposite edges are perpendicular , then the third pair is also perpendicular.

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To prove that in a tetrahedron, if two pairs of opposite edges are perpendicular, then the third pair is also perpendicular, we can follow these steps: ### Step 1: Define the Tetrahedron Let the tetrahedron be represented by the vertices A, B, C, and D. We can consider point A as the origin in a coordinate system. Therefore, we can define the position vectors of the points as follows: - \( \vec{A} = \vec{0} \) - \( \vec{B} = \vec{b} \) - \( \vec{C} = \vec{c} \) - \( \vec{D} = \vec{d} \)
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