In an inertial frame, the x, y, and z coordinates (in meters) of a particle P as
a function of time t (in seconds) are x = sin 3t, y = cost, and z = sin 2t. At t = 3s,
determine:
(a) (5pts) The velocity vector v in Cartesian coordinates, and the speed v.
(b) (5pts) The unit tangent vector uˆt
, unit binormal vector uˆb, and unit normal vector uˆn.
(c) (5pts) The angles \theta x, \theta y, \theta z that v makes with the x, y, and z axes (express in degrees).
(d) (5pts) The acceleration vector a in Cartesian coordinates.
(e) (5pts) The angles ϕx, ϕy, ϕz that a makes with the x, y, and z axes.
(f) (5pts) The angle \beta between v and a (express in degrees).