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Given a → , b → and c → are 3 vectors such that b → , c → are parallel unit vectors and a → = 3 . If a → + λ c → = 4 b → , then the sum of all the possible positive values of λ is

Correct answer

8

Step-by-step solution

a → = 4 b → - λ c → a → | 2 = 16 b → 2 + λ 2 c → 2 - 8 λ b → . c → 9 = 16 + λ 2 - 8 λ b → . c → ⇒ λ 2 - 8 λ + 7 = 0     as   b → ⋅ c → = 1 Sum of all the values of λ = 8

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