Consider the motion of a particle along a helix given by r(t) = sin t i +

Question:

Consider the motion of a particle along a helix given by r(t) = sin t i + cos t j + (t2 - 3t + 2)k, where the k component measures the height in meters above the ground and t ≥ 0.
a. Does the particle ever move downward?
b. Does the particle ever stop moving?
c. At what times does it reach a position 12 meters above the ground?
d. What is the velocity of the particle when it is 12 meters above the ground?