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JEE Main20264 April 2026Evening ShiftMathematicsThree Dimensional GeometryActual

If (2 +1, ^2-3 , -1 2 ) is the image of ( , 2 , 1) in the line x-2 3 = y-1 2 = z 1 , then the possible value(s) of is (are)

Options

  1. AOnly 3
  2. BOnly 3 and -1
  3. COnly 3 , 1 4 and -1
  4. DOnly 3 and 1 4

Correct answer

A. Only 3

Step-by-step solution

Let the given point be P = ( , 2 , 1) and its image be P' = (2 +1, ^2-3 , -1 2 ) . For P' to be the image of P in the given line L: x-2 3 = y-1 2 = z 1 , two conditions must be satisfied: 1. The midpoint of P and P' must lie on the line L . 2. The line segment PP' must be perpendicular to the line L . The midpoint M of P and P' is: M = ( + 2 + 1 2 , 2 + ^2 - 3 2 , 1 + -1 2 2 ) = ( 3 + 1 2 , ^2 - 2 , + 1 4 ) Since M lies on L , its coordinates must satisfy the equation of the line: 3 + 1 2 - 2 3 = ^2 - 2 - 1 2 = + 1

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