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JEE Main202124 Feb 2021Morning ShiftMathematicsVector AlgebraActual

Let three vectors a → , b → and c → be such that c → is coplanar with a → and b → , a → · c → = 7 and b → is perpendicular to c → , where a → = - i ^ + j ^ + k ^ and b → = 2 i ^ + k ^ , then the value of 2 a → + b → + c → 2 is

Correct answer

0

Step-by-step solution

Let c → = λ b → × a → × b → = λ b → · b → a → - b → · a → b → = λ 5 - i ^ + j ^ + k ^ + 2 i ^ + k ^ = λ - 3 i ^ + 5 j ^ + 6 k ^ c → · a → = 7 ⇒ 3 λ + 5 λ + 6 λ = 7 λ = 1 2 ∴   2 - 3 2 - 1 + 2 i ^ + 5 2 + 1 j ^ + 3 + 1 + 1 k ^ 2 = 2 1 4 + 49 4 + 25 = 25 + 50 = 75

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