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JEE Main202324 Jan 2023Evening ShiftMathematicsThree Dimensional GeometryActual

If the shortest distance between the lines x + 6 2 = y - 6 3 = z - 6 4 and x - λ 3 = y - 2 6 4 = z + 2 6 5 is 6 , then sum of squares of all possible values(s) of λ is

Correct answer

384

Step-by-step solution

Given equations are x - λ 3 = y - 2 6 4 = z + 2 6 5 is passing through a point λ , 2 6 , 3 6 and it's direction ratios are 3 , 4 , 5 . So, a → 1 = λ i ^ + 2 6 j ^ - 2 6 k ^ b → 1 = 3 i ^ + 4 j ^ + 5 k ^ And, x + 6 2 = y - 6 3 = z - 6 4 is passing through a point - 6 , 6 , 6 and it's direction ratios are 1 , 2 , 3 . a → 2 = - 6 i ^ + 6 j ^ + 6 k ^ b → 2 = 2 i ^ + 3 j ^ + 4 k ^ Now, a → 2 - a → 1 = - 6 i ^ + 6 j ^ + 6 k ^ - λ i ^ + 2 6 j ^ - 2 6 k ^ = -

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