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JEE Main202224 Jun 2022Morning ShiftMathematicsThree Dimensional GeometryActual

If the shortest distance between the lines r → = - i ^ + 3 k ^ + λ i ^ - a j ^ and r → = - j ^ + 2 k ^ + μ i ^ - j ^ + k ^ is 2 3 , then the integral value of a is equal to _____

Correct answer

0

Step-by-step solution

D.R. 's of a → 1 = - 1 , 0 , 3 D.R. 's of a → 2 = 0 , - 1 , 2 D.R. 's of b → 1 = 1 , - a , 0 D.R. 's of b → 2 = 1 , - 1 , 1 Now, a → 2 - a → 1 = i ^ - j ^ - k ^ and b → 1 × b → 2 = i ^ j ^ k ^ 1 - a 0 1 - 1 1 b → 1 × b 2 → = i ^ - a - j ^ + k ^ a - 1 i.e. b 1 → × b 2 → = a 2 + 1 + a - 1 2 So, a → 2 - a → 1 · b → 1 × b → 2 = 2 - 2 a Shortest distance between the lines, 2 1 - a a 2

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