Answer
Normal form of a line is:$\begin{bmatrix}{3 \\2}\end{bmatrix} \cdot \begin{bmatrix}{x_1 \\x_2}\end{bmatrix}=0$;
General form of the equation of a line is: $3x+2y=0$
Work Step by Step
The normal form of a line is: $n \cdot (x-p)=0$
and $n=\begin{bmatrix}{a \\b}\end{bmatrix}$
Here $a=3, b=2$
Now, the normal form of a line is:$\begin{bmatrix}{3 \\2}\end{bmatrix} \cdot \begin{bmatrix}{x_1 \\x_2}\end{bmatrix}=0$
The general form of an equation of a line is: $ax+by=c$
Thus, the general form of the equation of a line is: $3x+2y=c$
or, $3(0)+2(0)=c \implies c=0$
Hence, the normal form of a line is:$\begin{bmatrix}{3 \\2}\end{bmatrix} \cdot \begin{bmatrix}{x_1 \\x_2}\end{bmatrix}=0$;
The general form of the equation of a line is: $3x+2y=0$
