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Theorem 2: Algebraic Rules for Inner Products
Here is a list of algebraic rules for inner products. All the rules are easy to prove in either two or three dimensions. THEOREM 2 (Algebraic Rules for Inner Products) (i) A · i = a1, A · j = a2, A · k = a3. (ii) A · 0 = 0 · A = 0. (iii) A · B = B · A (Commutative Law). (iv) A · (B + C) = A · B + A · C (Distributive Law). (v) (tA) · B = t(A · B) (Associative Law). (vi) A · A = |A|2. PROOF Rule (vi) is proved as follows in three dimensions. A · A = a1a1 + a2a2 + a3a3 = a12 + a22 + a32 = |A|2. Inner products are useful in the study of perpendicular and parallel vectors.
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Last Update: 2006-11-06