Vector Equation

$R^2$

2D lines can be written if:

• Given Slope
• Given Point Or
• Given 2 Points Written in Standard Form or Slope Intercept Form

Vector Equation

$\vec{r}=\overrightarrow{r_0}+t\vec{m}$ or $[x,y]=[x_0,y_0]+t[m_1,m_2]$ Where:

• $\vec{r}=[x,y]$ and is a position vector to any point on line
• $\overrightarrow{r_0}=[x_0,y_0]$ and is the position vector to a known point
• $\vec{m}=[m_1,m_2]$ and is the direction vector

Creating Vector Equation Example

Closed Triangle Vector Addition Representation

Slope Equation

$m=\overrightarrow{[x_2-x_1,y_2-y_1]}$

$R^3$

Pretty much the same as in $R^2$ The formula of a 3d line can be determined if:

• Given slope
• Given point Or
• Given 2 Points

Vector Equation

$\vec{r}=\overrightarrow{r_0}+t\vec{m}$ or $[x,y,z]=[x_0,y_0,z_0]+t[m_1,m_2,m_3]$ Where:

• $r_0=[x_0,y_0,z_0]$ and is the position vector
• $\vec{m}=[m_1,m_2,m_3]$ and is the direction vector
• $tϵ\mathbb{R}$