"All limits, especially national ones, are contrary to the nature of mathematics… Mathematics knows no races… For mathematics the whole cultural world is a single country" – David Hilbert. "Face problems with a minimum of blind calculation, a maximum of seeing thought" – Hermann Minkowski

Distance from a point to a line using vectors – video clip

The distance from a point described by the vector s to the line

r = a + tb

is |(s−a)×b| if we make b a unit vector

or, more generally, |(s−a)×b|/|b|

This video works through an example carefully and clearly. Just one word of warning: the video uses a for the direction vector of the line (what we usually call b):