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SOLVED:The vertices of a tetrahedron correspond to four alternating corners of a cube. By using analytical geometry, demonstrate that the angle made by connecting two of the vertices to a point at the center of the cube is 109.5^{\circ}, the characteristic angle for tetrahedral molecules.
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SOLVED: Let be the tetrahedron in R^3 with vertices at the vectors e1, e2, and e3, and let' be the tetrahedron with vertices at vectors 0, V1, V2, and V3. See the figures to the right: Complete parts (a) and (b) below.Describe the linear transformation that maps onto'.If T is the linear transformation that maps onto', then the standard matrix for T, written in terms of V1, V2, and V3, is A = [L V1 V2 V3].Find the formula for the volume of the tetrahedron ' using the fact that the volume of S' is
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