Consider the tetrahedron formed by the four points P(0, 0, 0), Q(8, 0, 0), R(0,6, 0), and S(0, 0, 4). (a) Find the equations of the "top" plane formed by Q, R, and S and the "bottom" plane formed by P, Q, and R. (b) Sketch a graph of the 2D shadow onto the xy-plane. Be sure to label the axes and shade in the region. (c) Express the volume of the tetrahedron as a triple integral. Evaluate the triple integral to find the volume.
Consider the tetrahedron formed by the four points P(0, 0, 0), Q(8, 0, 0), R(0,6, 0), and S(0, 0, 4). (a) Find the equations of the "top" plane formed by Q, R, and S and the "bottom" plane formed by P, Q, and R. (b) Sketch a graph of the 2D shadow onto the xy-plane. Be sure to label the axes and shade in the region. (c) Express the volume of the tetrahedron as a triple integral. Evaluate the triple integral to find the volume.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.2: Ellipses
Problem 22E
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