(b) Suppose primitive vectors are constructed from the b; in the same manner (Eq. (5.3)) as...
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(b) Suppose primitive vectors are constructed from the b; in the same manner (Eq. (5.3)) as the bi are constructed from the a, Prove that these vectors are just the a themselves; i.e., show that b2 x b3 27 bị (b2 x b3) = a1, etc. (Hint: Write b, in the numerator (but not b2 ) in terms of the a;, use the vector identity Ax (Bx C) = B(A · C) – (A · B), and appeal to the orthogonality relations (5.4) and the result (5.15) above ) аз X аз bị = 27 a1 : (аz X аз) аз х а b2 = 27- aj (ад X аз) ај х а2 b3 = 27- aj (аэ X аз) b; satisfy 2 b; aj = 27dij (b) Suppose primitive vectors are constructed from the b; in the same manner (Eq. (5.3)) as the bi are constructed from the a, Prove that these vectors are just the a themselves; i.e., show that b2 x b3 27 bị (b2 x b3) = a1, etc. (Hint: Write b, in the numerator (but not b2 ) in terms of the a;, use the vector identity Ax (Bx C) = B(A · C) – (A · B), and appeal to the orthogonality relations (5.4) and the result (5.15) above ) аз X аз bị = 27 a1 : (аz X аз) аз х а b2 = 27- aj (ад X аз) ај х а2 b3 = 27- aj (аэ X аз) b; satisfy 2 b; aj = 27dij
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