Question

For what value(s) of a will the two points (1, a, 1) and (-3, 0, a) lie on opposite sides of the plane $3x+4y-12z+13=0$?

• A. $a<-1$ or $a>1/3$
• B. $a=0$ only
• C. 0 < a < 1
• D. -1 < a < 1

Answer 1

The correct option is A $a<-1$ or $a>1/3$

For given points to lie opposite sides of the plane $3x+4y-12z+13=0$ we should have,
$\left(3\right(1)+4(a)-12(1)+13)\left(3\right(-3)+4(0)-12(a)+13)<0$
$4(a+1)(4-12a)<0$
$(a+1)(3a-1)>0$
$\Rightarrow a<-1$ or $a>1/3$