Question

If $O$ be the origin and the coordinates of $P$ be $(1,2,-3)$, then the equation of the plane passing through $P$ and perpendicular to $OP$ is

• A. $x-2y+3z+12=0$
• B. $2x-3y-z-11=0$
• C. $x+2y-3z-14=0$
• D. $x+2y-3z=0$

Answer 1

The correct option is C $x+2y-3z-14=0$

Let the points be $O\left(0,0,0\right)$ and $P\left(1,2,-3\right)$.

The direction ratios of OP are,

$\left(1-0\right),\left(2-0\right),\left(-3-0\right)=\left(1,2,-3\right)$

The plane passing through $\left(x_1,y_1,z_1\right)$ is,

$a\left(x-x_1\right)+b\left(y-y_1\right)+c\left(z-z_1\right)=0$

$1\left(x-1\right)+2\left(y-2\right)-3\left(z+3\right)=0$

$x-1+2y-4-3z-9=0$

$x+2y-3z-14=0$