Question: how to find the equation of a line parallel to a vector?
Answer: To find the parametric equations of the line passing through the point (-1,2,3) and parallel to the vector <3,0,-1>, we first find the vector equation of the line. Here, r_0=<-1,2,3> and v=<3,0,-1>. Thus, the line has vector equation r=<-1,2,3>+t<3,0,-1>.