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

Question

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, 1, 2, 3, 4

MARKS App · Accepted Answer

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 → ⇒ x = S → · a → [ a → b → c → ] Taking dot with b → S → ⋅ b → = y a → b → c → ⇒ x = S → · b → [ a → b → c → ] Similarly z = S → · c → a → b → c → Hence S → = S → ⋅ a → b → × c → + S → ⋅ b → c → × a → + S → ⋅ c → a → × b → a → b → c → ⇒ r → = S → a → b → c → ⇒ r → = S → a → b → c → = 1 1 1 1 1 4 - 1 1 1 2 = 1 9 - 1 3 + 1 - 3 = 3

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