Suppose $\vec{r}(t)=\cos t\,\vec i + \sin t\, \vec j + 2 t\,\vec k$ represents the position of a particle on a helix, where $z$ is the height of the particle above the ground.

(a) Is the particle ever moving downward? ? yes no
If the particle is moving downward, when is this? When $t$ is in
(Enter none if it is never moving downward; otherwise, enter an interval or comma-separated list of intervals, e.g., (0,3], [4,5].)

(b) When does the particle reach a point 14 units above the ground?
When $t =$

(c) What is the velocity of the particle when it is 14 units above the ground?
$\vec v =$

(d) When it is 14 units above the ground, the particle leaves the helix and moves along the tangent. Find parametric equations for this tangent line (pick $t$ so that it is continuous through the time when the particle leaves the helix).
$x(t) =$ ,
$y(t) =$ ,
$z(t) =$