13. 

Let o: 1 -> R3 be a curve with acceleration 0. Prove that o is a line or a point. A point P in the first quadrant of R^2 moves such that its distance from the origin is equal to the slope of the line from the origin to P. Give a parametric representation of the curve traced by P using t as a parameter. Let P, and Q be two points on the sphere of radius 1. Assume that P * -Q. Show that there exists a curve joining P and Q on the sphere of radius 1, centered at the origin. Let o:[a,b]-> R^n be a smooth curve, if a:[0, L_{0}] -> R^n is the arclength reparametrization. Show that ||a (s)|| = 1.