Consider a straight line L which passes through a point A with position

vector a and is parallel to a vector b, as shown in Fig. 130, and let P be any point on L with position vector r.

Then from the vector triangle OAP, we see that




Now AP is parallel to b, so we may always find a scalar multiplier l, which

may be either positive or negative, such that

APl b:

Notice that l will be positive if P lies to the side of A toward which b is

directed; otherwise it will be negative.