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JEE Main20236 Apr 2023Morning ShiftMathematicsThree Dimensional GeometryActual

One vertex of a rectangular parallelopiped is at the origin O and the lengths of its edges along x , y and z axes are 3 , 4 and 5 units respectively. Let P be the vertex ( 3 , 4 , 5 ) . Then the shortest distance between the diagonal O P and an edge parallel to z axis, not passing through O or P is

Options

  1. A12 5
  2. B12 5
  3. C12 5 5
  4. D12 5

Correct answer

D. 12 5

Step-by-step solution

Given, One vertex of a rectangular parallelopiped is at the origin O and the lengths of its edges along x ,   y and z axes are 3 ,   4 and 5 units respectively, And P be the vertex ( 3 ,   4 ,   5 ) , Now plotting the diagram we get, Now equation of line O P : x 3 = y 4 = z 5 And equation of line A B : x - 3 0 = y 0 = z 1 Now finding, n 1 → × n 2 → = i ^ j ^ k ^ 3 4 5 0 0 1 ⇒ n 1 → × n 2 → = i ^ 4 - j ^ 3 + k ^ 0 ⇒ n 1 → × n 2 → = 4

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