Q55 / 90 · JEE Main 2012 (07 May Online) · Mathematics

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

  • A
    $0 < a < \frac{1}{3}$
  • B
    $-1 < a < 0$
  • C
    $a < -1$ or $a < \frac{1}{3}$
  • Correct answer
    D
    $a=0$

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. $\therefore$ We have $3+4(a)-12+13=0$ and $3(-3)-12(a)+13=0$ $\Rightarrow 4+4 a=0$ and $4-12 a=0$ $\Rightarrow a=-1$ and $a=\frac{1}{3}$ Since, $(1, a, 1)$ and $(-3,0, a)$ lie on the opposite sides of the plane $\therefore a=0$

Hence, the correct answer is option: 'D'.

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