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Problem Let a = ⟨ a 1 , a 2 , a 3 ⟩ \mathbf{a}=\langle a_1, a_2, a_3\rangle a = ⟨ a 1 , a 2 , a 3 ⟩ b = ⟨ b 1 , b 2 , b 3 ⟩ \mathbf{b}=\langle b_1, b_2, b_3\rangle b = ⟨ b 1 , b 2 , b 3 ⟩ a ⋅ b \mathbf{a}\cdot\mathbf{b} a ⋅ b a 1 2 + b 1 2 + a 2 2 + b 2 2 + a 3 2 + b 3 2 a_1^2 + b_1^2 + a_2^2 + b_2^2 + a_3^2 + b_3^2 a 1 2 + b 1 2 + a 2 2 + b 2 2 + a 3 2 + b 3 2 a 1 b 2 + a 2 b 3 + a 3 b 1 a_1b_2 + a_2b_3 + a_3b_1 a 1 b 2 + a 2 b 3 + a 3 b 1 a 1 b 1 + a 2 b 2 + a 3 b 3 a_1b_1 + a_2b_2 + a_3b_3 a 1 b 1 + a 2 b 2 + a 3 b 3 ( a 1 + b 1 ) ( a 2 + b 2 ) ( a 3 + b 3 ) (a_1 + b_1)(a_2 + b_2)(a_3 + b_3) ( a 1 + b 1 ) ( a 2 + b 2 ) ( a 3 + b 3 ) Browse the problem library