Given the module of vector a = 4, the module of B = 3, < A, b > = 3 / 3, find the module of (3a + 2b) & _; B, a + B If the module of vector a = 4, the module of B = 3, < A, b > = 3 / 3, find （3a+2b)•b Modules of a + B Modules of A-B

Because a * b = | a | * | B | * cos (π / 3) = 6, so (1) (3a + 2b) * b = 3A * B + 2B ^ 2 = 3 * 6 + 2 * 9 = 36; (2) from (a + b) ^ 2 = a ^ 2 + B ^ 2 + 2A * b = 16 + 9 + 12 = 37 to get | a + B | = √ 37; (3) from (a-b) ^ 2 = a ^ 2 + B ^ 2-2a * b = 16 + 9-12 = 13 to get | A-B | = √ 13

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