Question

The equation of plane passing through $(-1,0,1)$ and parallel to the plane $2x-3y+z+1=0,$ is

• A. $2x-3y+z+1=0$
• B. $3x-3y+2z+1=0$
• C. $-2x+3y+z-3=0$
• D. $x-3y+2z-1=0$

Answer 1

The correct option is A $2x-3y+z+1=0$

As required plane is parallel to $2x-3y+z+1=0$
So, normal vector is same
$\Rightarrow \overrightarrow{n}=2\hat{i}-3\hat{j}+\hat{k}$
Equation of plane is given by : $2x-3y+z+d=0$
it does pass through $(-1,0,1)$
$\Rightarrow -2-0+1+d=0\Rightarrow d=1$
$\therefore$ plane is $2x-3y+z+1=0$