Vì mặt phẳng (P) qua gốc tọa độ O nên gọi (P):$\text{ax}+by+cz=0$ ,$(\text{P) }$đi qua A suy ra $a+2b=0$ $\Leftrightarrow a=-2b$ $d(B;(\text{P))=d(}C;(P))\Leftrightarrow \left| 4b \right|=\left| 3c \right|$

$\Leftrightarrow \left[ \begin{align} & 4b=3c=-2a \\ & -4b=3c=2a \\ \end{align} \right.$ $\Leftrightarrow \left[ \begin{align} & a=6;b=-3;c=-4 \\ & a=6;b=-3;c=4 \\ \end{align} \right.$

$\Leftrightarrow \left[ \begin{align} & (P):6x-3y-4z=0 \\ & (P):6x-3y+4z=0 \\ \end{align} \right.$