Let 2 a → = b → × c → + 2 b → where a → , b → and c → are three unit vectors, then sum of all possible values of 3 a → + 4 b → + 5 c → is

Question

Let 2 a → = b → × c → + 2 b → where a → , b → and c → are three unit vectors, then sum of all possible values of 3 a → + 4 b → + 5 c → is, 10, 12, 14, 16

MARKS App · Accepted Answer

2 a → = b → × c → + 2 b → Taking dot with b → 2 a → ⋅ b → = 2 b → 2 ⇒ a → ⋅ b → = 1 ⇒ a → = b → also b → × c → = 0 (from given equation) ⇒ b → = c → or b → = - c → So, if b → = c → , then 3 a → + 3 b → + 5 c → = 12 or if b → = - c → , then 3 a → + 4 b → + 5 c → = 2

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