MHT CET202616 April 2026Evening ShiftMathematicsVector AlgebraActual

If a = 4 i + j + k , b = 2 i + j + 2 k and c = 3 i + 4 j + 5 k , then ( a + b ) ( b + c ) =

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Correct answer

C. 61

Step-by-step solution

Given vectors are a = 4 i + j + k , b = 2 i + j + 2 k and c = 3 i + 4 j + 5 k . Calculating a + b : a + b = (4+2) i + (1+1) j + (1+2) k = 6 i + 2 j + 3 k Calculating b + c : b + c = (2+3) i + (1+4) j + (2+5) k = 5 i + 5 j + 7 k Taking the dot product: ( a + b ) ( b + c ) = (6 i + 2 j + 3 k ) (5 i + 5 j + 7 k ) = (6 5) + (2 5) + (3 7) = 30 + 10 + 21 = 61 Answer: 61

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