Vectors occur in the study of crystallography. Now we can let V1, V2, and v3 be noncoplanar vectors. From these vectors, we create V2 x V3 V3 X V1 V1 X V2 k1 k2= k3 V (V2 x V3)) V1 (V2 x V3)' V1 (V2 x V3) Vectors written in the form niv+n2v2 + n3v3 where n is an integer, form the lattice for a crystal. If we write vectors as a linear combination of k, k2, k3, then these form the reciprocal lattice. (a) Show that each k is orthogonal to v, as long as i and j are different. (b) Determine the product kv, for each i = 1,2,3. (c) Show the triple scalar product of the k vectors satisfies: 1 k. (k2 x k3) V1 (V2 x V3)