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JEE Main202324 Jan 2023Morning ShiftMathematicsThree Dimensional GeometryActual

The shortest distance between the lines x - 2 3 = y + 1 2 = z - 6 2 and x - 6 3 = 1 - y 2 = z + 8 0 is equal to ______

Correct answer

0

Step-by-step solution

Given equations are x - 2 3 = y + 1 2 = z - 6 2 is passing through a point 2 , - 1 , 6 and it's direction ratios are 3 , 2 , 2 . So, a → 1 = 2 i ^ - j ^ + 6 k ^ b → 1 = 3 i ^ + 2 j ^ + 2 k ^ And, x - 6 3 = y - 1 - 2 = z + 8 0 is passing through a point 6 , 1 , - 8 and it's direction ratios are 3 , - 2 , 0 . a → 2 = 6 i ^ + j ^ - 8 k ^ b → 2 = 3 i ^ - 2 j ^ + 0 k ^ Now, a → 2 - a → 1 = 4 i ^ + 2 j ^ - 14 k ^ b → 1 × b → 2 = i ^ j ^ k ^ 3 2 2 3 - 2 0 &#8658

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