Line and Plane — Maths STD 12 Science — Question

We know that the vector equation of a plane passing through a point  
$A(\bar{a})$ and normal to $\bar{r} \cdot \bar{n}=\bar{a} \cdot \bar{n}$
Here $\bar{a}=3 \hat{i}-2 \hat{j}+\widehat{k}$ and $\widehat{n}=4 \hat{i}+3 \hat{j}+2 \widehat{k}$
The vector equation of the required plane is
$\bar{r} \cdot \bar{n}=\bar{a} \cdot \bar{n}$
$\bar{r} \cdot(4 \hat{i}+3 \hat{j}+2 \widehat{k})=(3 \hat{i}-2 \hat{j}+\widehat{k}) \cdot(4 \hat{i}+3 \hat{j}+2 \widehat{k})$
$\bar{r} \cdot(4 \hat{i}+3 \hat{j}+2 \widehat{k})=12-6+2$
$\bar{r} \cdot(4 \hat{i}+3 \hat{j}+2 \widehat{k})=8$
The vector equation of the required plane is $\bar{r} \cdot(4 \hat{i}+3 \hat{j}+2 \widehat{k})=8$