If , , and are noncoplanar vectors, let k3 v1 v2 v1 v2 v3
Chapter 12, Problem 12.221(choose chapter or problem)
If , , and are noncoplanar vectors, let k3 v1 v2 v1 v2 v3 k2 v3 v1 v1 v2 v3 k1 v2 v3 v1 v2 v3 v1 v2 v3 (These vectors occur in the study of crystallography. Vectors of the form , where each is an integer, form a lattice for a crystal. Vectors written similarly in terms of , , and form the reciprocal lattice.) (a) Show that is perpendicular to if . (b) Show that for . (c) Show that . k1 k2 k3 1 v1 v2 v3 ki vi
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