Consider a regular tetrahedron with edge length one (4 equilateral triangles joined edge to edge) call it T. Set T on the x, y-plane with a vertex at the origin and an edge aligned with the positive x-axis. Call the three edges that touch the origin vectors i,f, and g, where vector i = (1,0,0), vector f = (1, p3,0). (Why?)
a) Find vector g using vector methods. b) Find the equation for the plane that contains the face of T not touching the origin. c) Find the coordinates for the center of T. Use symmetry whenever possible. d) Find the angle between a pair of vectors having their tails at the center of T and their heads on any two vertices of T. Think of the methane molecule with carbon at the center and the four hydrogens at the vertices. You have found the bond angle.