   Chapter 11.3, Problem 73E

Chapter
Section
Textbook Problem

# Bond AngleConsider a regular tetrahedron with vertices ( 0 , 0 , 0 ) , ( k , k , 0 ) , ( k , 0 , k ) and ( 0 , k , k ) , where k is a positive real number.(a) Sketch the graph of the tetrahedron.(b) Find the length of each edge.(c) Find the angle between any two edges.(d) Find the angle between the line segments from the centroid ( k / 2 , k / 2 , k / 2 ) to two vertices. This is the bond angle for a molecule, such as CH 4 (methane) or PbCl 4 (lead tetrachloride), where the structure of the molecule is a tetrahedron.

(a)

To determine

To Graph: The graph of the regular tetrahedron whose vertices are (0,0,0),(k,0,k),(k,0,k), and (0,k,k).

Explanation

Given:

The regular tetrahedron with vertices (0,0,0),(k,0,k),(k,0,k), and (0,k,k), where k is a real positive number.

Graph:

Consider a regular tetrahedron with vertices (0,0,0),(k,0,k),(k,0,k), and (0,k,k)

(b)

To determine

To Calculate: The length of each edge of the regular tetrahedron whose vertices are (0,0,0),(k,0,k),(k,0,k), and (0,k,k).

(c)

To determine

To calculate: The angle between any two edges.

(d)

To determine

To Calculate: The angle between the line segments from the centroid (k/2,k/2,k/2) to the two vertices.

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