37 Suppose that AB, AC, and AD are directed line segments of u, v, and u + v, respectively, with ju|=|v|. Show that AD bisects the angle between AB and AC. 38 Let P be a vertex of a cube. Draw a diagonal of the cube from P and a diagonal of one of the faces from P. Use vectors to find the cosine of the angle between these two diagonals. 39 Use vectors to find the cosine of the angle between two faces of a regular tetrahedron. (See Problem 33, Chapter 13, Section 2.)

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