In this video I show you how to find the closest point and shortest distance from the origin to a line.

I use the following example to demonstrate this.

    \[\begin{array}{l} {\rm{If  }}l:{\bf{r}} = \left( {\begin{array}{*{20}{c}} { - 3}\\ 3\\ { - 1} \end{array}} \right) + \lambda \left( {\begin{array}{*{20}{c}} 1\\ { - 3}\\ 2 \end{array}} \right)\\ \end{array}\]

Find the closest point on the line l to the origin and the shortest distance.