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JEE Main202120 Jul 2021Morning ShiftMathematicsThree Dimensional GeometryActual

If the shortest distance between the lines r 1 → = α i ^ + 2 j ^ + 2 k ^ + λ i ^ - 2 j ^ + 2 k ^ , λ ∈ R , α > 0 and r 2 → = - 4 i ^ - k ^ + μ 3 i ^ - 2 j ^ - 2 k ^ , μ ∈ R is 9 , then α is equal to_____.

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We have, r 1 → = α i ^ + 2 j ^ + 2 k ^ + λ i ^ - 2 j ^ + 2 k ^ r 2 → = - 4 i ^ - k ^ + μ 3 i ^ - 2 j ^ - 2 k ^ If r → = a → + λ b → and r → = c → + λ d → , then shortest distance between two lines is L = a → - c → · b → × d → b → × d → Here, b → × d → = i ^ j ^ k ^ 1 - 2 2 3 - 2 - 2 ⇒ b → × d → = 8 i ^ + 8 j ^ + 4 k ^ ⇒ b → × d → =

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