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JEE Main20204 Sep 2020Evening ShiftMathematicsThree Dimensional GeometryActual

The distance of the point ( 1 , - 2 , 3 ) from the plane x - y + z = 5 measured parallel to the line x 2 = y 3 = z - 6 is :

Options

  1. A7 5
  2. B1
  3. C1 7
  4. D7

Correct answer

B. 1

Step-by-step solution

Equation PQ x - 1 2 = y + 2 3 = z - 3 - 6 = λ Let Q ≡ ( 2 λ + 1 , 3 λ - 2 , - 6 λ + 3 ) Q lies on x - y + z = 5 ⇒    ( 2 λ + 1 ) - ( 3 λ - 2 ) + ( - 6 λ + 3 ) = 5 ⇒ λ = 1 7 ⇒ Q ≡ 9 7 , - 11 7 , 15 7 PQ = 1 - 9 7 2 + - 2 + 11 7 2 + 3 - 15 7 2 = 1

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