Lets say you have $\vec{a}$(2,1) and $\vec{b}$(0,3)
Are these lines the same?
$ L_1 = \{\vec{b} + t_1 (\vec{b}-\vec{a}) \mid t_1 \in\mathbb{R} \}$
$ L_2 = \{\vec{a} + t_2 (\vec{b}-\vec{a}) \mid t_2 \in\mathbb{R} \}$
Lets say you have $\vec{a}$(2,1) and $\vec{b}$(0,3)
Are these lines the same?
$ L_1 = \{\vec{b} + t_1 (\vec{b}-\vec{a}) \mid t_1 \in\mathbb{R} \}$
$ L_2 = \{\vec{a} + t_2 (\vec{b}-\vec{a}) \mid t_2 \in\mathbb{R} \}$
$\begin{array}{lcl} L_2 & = &\{ a + t_2(b-a) & \mid t_2 \in\mathbb{R} \} \\ & = &\{ (b-b)+ a + t_2(b-a)&\mid t_2 \in\mathbb{R} \} \\ & = &\{b + (t_2-1)(b-a)&\mid t_2 \in\mathbb{R}\} \\ & = &\{b + t'(b-a)& \mid t' \in \mathbb{R}\} \\ & = &L_1 \end{array}$