The position vector for a particle moving on a helix is c(t) = (3 cos(t), 2 sin(t), t²). (a) Find the speed of the particle at time to = 4. (b) Is c'(t) ever orthogonal to c(t)? O Yes, when t is a multiple of T. O Yes, when t = 0. O No (c) Find a parametrization for the tangent line to c(t) at to = 47. (Enter your answer as a comma-separated list of equations in (x, y, z) coordinates.) (d) Where will this line intersect the xy-plane? =([ (x, y, z) =

Sketch the parametric curve of r(t) = (2cost,2sint.3) Then, find and draw the tangent vector r'(0).

Question 10 described by the vector function r(t) = (4t² Int, -2e-3t). t-4 Consider the curve which is 29 a) Find the integral ſ r(t)dt. b) Find parametric equations for the tangent line to the given curve at the point (0, -3, -2e-³). c) Can you find parametric equations for the tangent line to the given curve at the point (0, -2,-2)?

Q1/ Find the curve unit tangent vector and length of the indicated portion of the curve r(t) = (9 sin 2t)i + (6cos 2t)j + 5t k