Answer Happy

Suppose 𝑟⃗ (𝑡)=cos𝑡𝑖⃗ +sin𝑡𝑗⃗ +3𝑡𝑘⃗ r→(t)=cos⁡ti→+sin⁡tj→+3tk→ representsthe position of a particle on a helix, where 𝑧z is theheight of the particle above the ground. *i can't readcursive
(1 point) Suppose r(t) = costi + sint 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? no If the particle is moving downward, when is this? When t is in none (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 20 units above the ground? When t = 20 3 (c) What is the velocity of the particle when it is 20 units above the ground? v = -sin (20); 2300); 20 3 (d) When it is 20 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). 20 x(t) = COS 20 + cos y(t) = sin z(t) = 20 + 3t - t sin + t cos + 3k 20 " "