LinePoint

A Line and a Point has the following questions to answer.

1. Does the Point belong to the Line?
2. What point of the Line is closest to the given Point?
3. What is is the distance between the Point and the Line (its closest point)?

Fig.1. Vectors a and b, a - b, and representing them as sum of orthogonal vectors.

If we have a Point B and a Line, which is defined by a Point P on it and a Vector v, see Fig.1, then from a comparison with wikipage Vectors we can write how to find the Point C for the question 2 above.
.. math::
PC = P + v (PB \dot V) \div (v \dot v)

OK