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JEE Main202325 Jan 2023Evening ShiftMathematicsThree Dimensional GeometryActual

If the shortest distance between the line joining the points 1 , 2 , 3 and 2 , 3 , 4 , and the line x - 1 2 = y + 1 - 1 = z - 2 0 is α , then 28 α 2 is equal to _____ .

Correct answer

0

Step-by-step solution

Equation of line joining 1 , 2 , 3 and 2 , 3 , 4 is r → = i ^ + 2 j ^ + 3 k ^ + λ i ^ + j ^ + k ^ Also, vector equation is r → = i ^ - j ^ + 2 k ^ + μ 2 i ^ - j ^ So, a → 1 = i ^ + 2 j ^ + 3 k ^ a → 2 = i ^ - j ^ + 2 k ^ Hence, a → 2 - a → 1 = 0 i ^ - 3 j ^ - k ^ And, b → 1 = i ^ + j ^ + k ^ b → 2 = 2 i ^ - j ^ + 0 k ^ And, b → 1 × b → 2 = i ^ j ^ k ^ 1 1 1 2 - 1 0 = i ^ + 2 j ^ - 3 k ^ ⇒ b → 1 × b → 2 = 14 Required sh

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