Question

The equation of the plane passing through $(3,4,-1)$ and parallel to the plane $2x-3y+5z-7=0$ is

• A. $2x-3y+5z+15=0$
• B. $2x-3y+5z+9=0$
• C. $2x-3y+5z+11=0$
• D. $2x-3y-5z-13=0$

Answer 1

The correct option is C $2x-3y+5z+11=0$

$p_1:2x-3y+5z-7=0$ and $A(3,4,-1)$
Let the required plane be $p_2$
As plane $p_2$ is parallel to $p_1,$ hence it's normal will be same as that of $p_1$
$\therefore$ the equation of plane $p_2$ is
$\Rightarrow 2x-3y+5z+\lambda =0\cdots \left(i\right)$
Since, the plane passes through $A(3,4,-1)$
$\therefore 2\left(3\right)-3\left(4\right)+5(-1)+\lambda =0$
$\Rightarrow \lambda =11$
Putting the value of $\lambda$ in $\left(i\right),$ we get
$2x-3y+5z+11=0$