Let a → = i ^ + 2 j ^ - k ^ , b → = i ^ - j ^ and c → = i ^ - j ^ - k ^ be three given vectors. If r → is a vector such that r → × a → = c → × a → and r → · b → = 0 , then r → · a → is equal to

Question

Let a → = i ^ + 2 j ^ - k ^ , b → = i ^ - j ^ and c → = i ^ - j ^ - k ^ be three given vectors. If r → is a vector such that r → × a → = c → × a → and r → · b → = 0 , then r → · a → is equal to,

MARKS App · Accepted Answer

r → - c → × a → = 0 ⇒ r → = c → + λ a → taking dot product with b → Now, 0 = b → · c → + λ a → · b → ⇒ λ = - b → · c → a → · b → = - 2 - 1 = 2 So, r → · a → = a → · c → + 2 a → 2 = 0 + 2 × 6 = 12

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