I was reading through my textbook on parametric equations and I came across the following question:
(a) Find parametric equations and symmetric equations of the line that passes through the points A(2,4,-3) and B(3,-1,1).
The solution is as follows:
Solution: We are not explicitly given a vector parallel to the line, but observe that the vector with representation, AB is parallel to the line, and v= (1,-5,4)
Thus, direction numbers are a=1, b=-5, and c=4. Taking the point (2,4,-3) as Po we see the that the parametric equations are x=2+t, y=4-5t, z=-3+4t.
My question is: Why is vector v parallel to the line? It seems all that was done was calculate A-B, the difference of the vectors, but that doesn't show why v would be parallel.