When does the particle reach a point 18 units above the

Question

Suppose r^→(t) = cos t_i^→ + sin t_j^→ + 3t_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? When? (If the particle is never moving downward, enter DNE.)

b. When does the particle reach a point 18 units above the ground?

c. What is the velocity of the particle when it is 18 units above the ground? (Round each component to three decimal places.)

d. When it is 18 units above the ground, the particle leaves the helix and moves along the tangent line. Find parametric equations for this tangent line. (Round each component to three decimal places.)