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The lengths of two opposite edges of a tetrahedron of `aa n db ;` the shortest distane between these edgesis `d ,` and the angel between them if `thetadot` Prove using vector4s that the volume of the tetrahedron is `(a b di s ntheta)/6` .

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To prove that the volume of the tetrahedron is given by the formula \( V = \frac{1}{6} A B D \sin \theta \), we will follow these steps: ### Step 1: Understand the Geometry of the Tetrahedron We have a tetrahedron with vertices \( O, A, B, \) and \( C \). The lengths of two opposite edges, \( OA \) and \( BC \), are given as \( A \) and \( B \) respectively. The shortest distance between these edges is \( D \), and the angle between them is \( \theta \). **Hint:** Visualize the tetrahedron and identify the edges and the angle between them. ### Step 2: Position Vectors ...
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