Please help me answer these homework questions.

Conceptual Problems 3 1. Suppose that ri(1) and 12(1) are two curves which intersect at a point P. If P = ri(41) and P = 12(42), does this mean that 41 = 12? If so, briefly explain why. If not, give a counterexample. 2. Suppose that r1 (() is the equation of a curve and one defines r2(1) = ri(At) for A a positive constant (basically 12 is using a different "time scale" than the one used for r1). How is the velocity vector of 12 related to the one of ry? What about the acceleration vectors? If one defines r3(1) = ri(1 - 40), how is the velocity vector of 13 related to the one of r? What about the acceleration vectors? Make sure you justify your answers. 3. Is the velocity vector v(1) of a curve r() always perpendicular to the acceleration vector a()? If so, briefly explain why. If not, give a counterexample. 4. Suppose that r(1) is a vector valued function, v() is its velocity, and a() is its acceleration, all functions defined for all / E (-0o, co). Assume r(1) x v(1) = c for all ( E (-0o, 00), where c is a constant vector. Show that r() and a(1) are parallel for all ( E (-0o, co). Give an explicit example of a path r(() such that I(1) = -2(1). RedmiBook F3 F4 F5 F6 F7 F9 F10 Prison % # E R U P