Question

Equation of plane passing through the points $(2,2,1)$ , $(9,3,6)$ and perpendicular to the plane $2x+6y+6z-1=0$ , is

• A. $3x+4y+5z=9$
• B. $3x+4y-5z+9=0$
• C. $3x+4y-5z-9=0$
• D. None of these

Answer 1

Answer: (C)

Equation of a plane passing through $(2,2,1)$ is $a(x-2)+b(y-2)+c(z-1)=0$ ... (i)
This passes through $(9,3,6)$ and is perpendicular to $2x+6y+6z-1=0$
$\therefore$ $7a+b+5c=0$ and $2a+6b+6c=0$
On solving above equations by cross-multiplication, we get
$\Rightarrow$ $\frac{a}{6-30}=\frac{-b}{42-10}=\frac{c}{42-2}$
$\Rightarrow$ $\frac{a}{-24}=\frac{b}{-32}=\frac{c}{40}$
$\Rightarrow$ $\frac{a}{-3}=\frac{b}{-4}=\frac{c}{5}$
On substituting the values of
$a,b$ and $c$ in Eq. (i),
we get $-3(x-2)-4(y-2)+5(z-1)=0$ or $3x+4y-5z-9=0$
as the required plane.