Q. For what value(s) of $a$, will the two points $(1,\ a,\ 1)$ and $( - 3,0,\ a)$ lie on opposite sides of the plane $3x + 4y - 12\mathcal{z} + 13 = 0?$
A) $a < - 1$ or $a > 1/3$
B) $a = 0$ only
C) $0 < a < 1$
D) $- 1 < a < 1$
Explanation
(a)
We must have $(3 + 4a - 12 + 13)( - 9 - 12a + 13) < 0$
$\Rightarrow (a + 1)(12a - 4) > 0$
$\Rightarrow a < - 1$ or $a > 1/3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.