JEE Main2016MathematicsThree Dimensional GeometryActual

If the line, x - 3 2 = y + 2 - 1 = z + 4 3 lies in the plane l x + m y - z = 9 , then l 2 + m 2 is equal to

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Correct answer

B. 2

Step-by-step solution

x - 3 2 = y + 2 - 1 = z + 4 3 lies in l x + m y - z = 9 The point ( 3 , − 2 , − 4 ) lies on the plane. So it should satisfy the equation of the plane. 3 l - 2 m + 4 = 9 3 l - 2 m = 5 .......(i) ∴ Line lies in plane ∴ line is perpendicular to the normal to the plane 2 l - 1 . m - 3 = 0 2 l - m = 3 .......(ii) l = 1 and m = - 1 ∴ l 2 + m 2 = 1 + 1 = 2

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