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JEE Main202116 Mar 2021Evening ShiftMathematicsThree Dimensional GeometryActual

If the distance of the point 1 , - 2 , 3 from the plane x + 2 y - 3 z + 10 = 0 measured parallel to the line, x - 1 3 = 2 - y m = z + 3 1 is 7 2 , then the value of m is equal to _______.

Correct answer

0

Step-by-step solution

DC of line ≡ 3 m 2 + 10 , - m m 2 + 10 , 1 m 2 + 10 Q ≡ 1 + 3 r m 2 + 10 , - 2 + - m r m 2 + 10 , 3 + r m 2 + 10 Q lies on x + 2 y - 3 z + 10 = 0 1 + 3 r m 2 + 10 - 4 - 2 m r m 2 + 10 - 9 - 3 r m 2 + 10 + 10 = 0 ⇒ r m 2 + 10 3 - 2   m - 3 = 2 ⇒ r m 2 + 10 - 2   m = 2 r 2 m 2 = m 2 + 10 7 2   m 2 = m 2 + 10 ⇒ 5 2   m 2 = 10 ⇒ m 2 = 4 m = 2

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