Sunday, March 31, 2013
Parametric Representation of Lines
Line in \(\mathbb{R}^2\):
\(y = mx + b \)Line in \(\mathbb{R}^n\):
\(L = { \vec{x} + t \vec{v} | t \in \mathbb{R} } \)Given two point vectors \(\vec{P_1}\) and \(\vec{P_2}\), what is the line that passes through them ?
Solution:
\( L = \vec{P_1} + t(\vec{P_1} - \vec{P_2}) | t \in \mathbb{R} \)or
\( L = \vec{P_2} + t(\vec{P_1} - \vec{P_2}) | t \in \mathbb{R} \)See video.
