(a) Show that the line through OA is orthogonal to the plane containing the face BCD. Deduce that the line containing the origin and any vertex is orthogonal to the plane containing the other three vertices (without checking this case-by-case). (b) Show that the angle between the planes containing the faces ABC and BCD is cos ¹(3). Explain why it follows that the angle between the planes containing any two faces is cos-¹(¹). (c) Find the angle between the line through the edge AB and the plane containing the face BCD, correct to 2 decimal places.
(a) Show that the line through OA is orthogonal to the plane containing the face BCD. Deduce that the line containing the origin and any vertex is orthogonal to the plane containing the other three vertices (without checking this case-by-case). (b) Show that the angle between the planes containing the faces ABC and BCD is cos ¹(3). Explain why it follows that the angle between the planes containing any two faces is cos-¹(¹). (c) Find the angle between the line through the edge AB and the plane containing the face BCD, correct to 2 decimal places.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter12: Conic Sections
Section12.1: Parabolas
Problem 1E: A parabola is the set of all points in the plane that are equidistant from a fixed point called the...
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Transcribed Image Text:4. A regular tetrahedron has vertices at the points A = (1, 1, 1), B = (1, −1, −1),
C = (-1, 1, -1) and D = (−1, −1, 1).
(a) Show that the line through OA is orthogonal to the plane containing the face
BCD. Deduce that the line containing the origin and any vertex is orthogonal to
the plane containing the other three vertices (without checking this case-by-case).
(b) Show that the angle between the planes containing the faces ABC and BCD is
cos¯¹ (¹). Explain why it follows that the angle between the planes containing
any two faces is cos¯¹ (3).
(c) Find the angle between the line through the edge AB and the plane containing
the face BCD, correct to 2 decimal places.
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