Finding the shortest distance from a given point to a line given the vector equation. Very common question in MATH 115: Linear Algebra for Engineering at University of Waterloo.
Nice. A tip for the future, start off with the most central, interesting and motivating information, namely drawing the shortest distance from point P( 3,3,1), and from the start telling that the closest distance must be a line perpendicular to line L. THEN you construct the vector equations that gives you that sought vector ( the perpendicular one ) and the distance along it from 3,3,1 to the line.
