Let a → = i ^ + j ^ + k ^ , b → = i ^ + 4 j ^ - k ^ and c → = i ^ + j ^ + 2 k ^ . If S → be a unit vector, then the magnitude of the vector a → ⋅ S → b → × c → + b → ⋅ S → c → × a → + c → ⋅ S → a → × b → is equal to

Step-by-step solution

Let r → = a → ⋅ S → b → × c → + b → ⋅ S → c → × a → + c → ⋅ S → a → × b → S → can be written as a linear combination of b → × c → , c → × a → , a → × b → S → = x b → × c → + y c → × a → + z a → × b → Taking dot with a → S → ⋅ a → = x a → b → c → ⇒