Suppose that the position r(t) and velocity v(t) of a moving object satisfy r(t) . v(t) = 0 for all t. What does this imply about the curve r(t)?
A) The curve lies on a sphere centred at the origin.
B) The curve lies in a plane.
C) The curve is a circle.
D) The curve is a helix.
E) The curve lies on a hyperboloid.

Question

Quizplus · Accepted Answer

The condition r(t) . v(t) = 0 implies that the position vector r(t) is always perpendicular to the velocity vector v(t). This means that the object is moving in such a way that its distance from the origin remains constant, which is characteristic of motion on the surface of a sphere centered at the origin.

Suppose That the Position R(t) and Velocity V(t) of a Moving