## Linear Algebra: A Modern Introduction

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: $3x+2y=0$
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: $3x+2y=0$