Trong không gian Oxyz, cho mặt phẳng (P): 2x - 2y + z + 2021 = 0

* Hướng dẫn giải

Đường thẳng $d:\frac{x}{1}=\frac{y-2}{1}=\frac{z+6}{-2}$ có 1 VTCP là $\overrightarrow{u_d}=\left(1;1;-2\right).$

Mặt phẳng $\left(P\right):2x-2y+z+2021=0$ có 1 VTPT là $\overrightarrow{n_P}=\left(2;-2;1\right).$

Vì $\left\{\begin{array}{l}d\subset \left(Q\right)\\ \left(P\right)\perp \left(Q\right)\end{array}\right.\Rightarrow \left\{\begin{array}{l}\overrightarrow{u_d}\perp \overrightarrow{n_Q}\\ \overrightarrow{n_P}\perp \overrightarrow{n_Q}\end{array}\right.\Rightarrow \overrightarrow{n_Q}=\left[\overrightarrow{u_d},\overrightarrow{n_P}\right]=\left(-3;-5;-4\right).$

Ta có $M\left(0;2;-6\right)\in d.$ Vì $d\subset \left(Q\right)\Rightarrow M\in \left(Q\right).$

Suy ra phương trình mặt phẳng (P) là $-3x-5\left(y-2\right)-4\left(z+6\right)=0\iff -3x-5y-4z-14=0.$

$\Rightarrow a=-3,b=-5,c=-4.$

Vậy $a+b+c=-3-5-4=-12.$

Chọn A.