Perpendicular Diagonals and a Dihedral Angle in a Right Prism

★ 5/10solid geometry Triangle Geometry vectors

Problem

As shown in the figure, the right prism $ABC\text{-}A_1B_1C_1$ (its lateral edges perpendicular to the base) has volume $1$ . In the base triangle, $AB \perp BC$ , $AB = 2$ , and $BC = 1$ .

1. Prove that $BC_1 \perp A_1C$ . 2. Find the cosine of the dihedral angle $B_1\text{-}A_1C\text{-}B$ .

Answer

Solution

Difficulty	5/10
Topics	solid geometry, Triangle Geometry, vectors

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