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JEE Main202313 Apr 2023Morning ShiftMathematicsThree Dimensional GeometryActual

Let the image of the point 5 3 , 5 3 , 8 3 in the plane x - 2 y + z – 2 = 0 be P . If the distance of the point Q ( 6 , - 2 , α ) , α > 0 , from P is 13 , then α is equal to _ _ _ _ _ _ _ .

Correct answer

0

Step-by-step solution

The image of the point 5 3 , 5 3 , 8 3 w.r.t plane will be, x - 5 3 1 = y - 5 3 - 2 = 2 - 8 3 1 = - 2 1 × 5 3 - 2 × 5 3 + 8 3 - 2 1 2 + 2 2 + 1 2 ⇒ x - 5 3 1 = y - 5 3 - 2 = 2 - 8 3 1 = - 2 ( - 1 ) 6 ⇒ P ( x ,   y ,   z ) = ( 2 , 1 , 3 ) But P Q = 13 4 2 + 3 2 + ( α - 3 ) 2 = 169 | α - 3 | = 12 α = 15 Since α > 0 Hence this is the required answer.

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