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

The correct option is C $3x+4y-5z-9=0$

Let $ax+by+cz=1$ be a plane
Since, it is perpendicular to $2x+6y+6z=1$
Therefore, $2a+6b+6c=1$ ....(1)
and passes through $(2,2,1)$ & $(9,3,6)$
Therefore, $2a+2b+c=1$ ....(2)
and $9a+3b+6c=1$ ....(3)
Solving $\left(1\right),\left(2\right)$ and $\left(3\right)$ simultaneoulsly, we get
$a=\frac{3}{9}$, $b=\frac{4}{9}$, $c=-\frac{5}{9}$
Therfore, desired plane is $3x+4y-5z-9=0$
Ans: C