JEE Main2012MathematicsThree Dimensional GeometryActual

The values of a for which the two points (1, a, 1) and (-3,0, a) lie on the opposite sides of the plane 3 x+4 y-12 z+13=0 , satisfy

Options

A0 < a < 1 3
B-1 < a < 0
Ca < -1 or a < 1 3
Da=0

Correct answer

D. a=0

Step-by-step solution

Given equation of plane is 3 x+4 y-12 z+13=0 (1, a, 1) and (-3,0, a) satisfy the equation of plane. We have 3+4(a)-12+13=0 and 3(-3)-12(a)+13=0 4+4 a=0 and 4-12 a=0 a=-1 and a= 1 3 Since, (1, a, 1) and (-3,0, a) lie on the opposite sides of the plane a=0

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