Vector Form : The equation of the plane, which passes through $\vec{a}$ and normal to $\vec{n}$ is $(\vec{r}-\vec{a})\cdot\vec{n}=0$ Here $\vec{a}=\hat{i}-\hat{2k}$ and $\vec{n}=\hat{i}+\hat{j}-\hat{k}$ ∴ The equation of the plane is $(\vec{r}-\vec{a})\cdot\vec{n}=0$ i.e., $[\vec{r}-(\hat{i}-\hat{2k})]\cdot(\hat{i}+\hat{j}-\hat{k})=0$Cartesian Form :If < a, b, c > are direction ratios of the normal to the plane, then the equation of the plane through (x, y, z) is $a(x - x_1) + b(y - y_1) + c(z - z_1) = 0$.This passes through (1, 0, – 2),$\therefore x1 = 1, y_1 = 0, z_1 = -2$.Direction ratios of normal $\hat{i}+\hat{j}-\hat{k}$ are < 1, 1, –1 >∴ a = 1, b = 1, c = – 1∴ The equation of the plane is :1 (x – 1) + 1 (y – 0) – 1 (z + 2) = 0⇒ x – 1 + y – z – 2 = 0 ⇒ x + y – z = 3.