The position vector of a particle moving through space is r(t) = (t − sin t)i + (1 − cost)j + t k, t ≥ 0.

(a) (5 points) Find the velocity and acceleration vectors and the speed as a function of t.

(b) (5 points) Find the parametric equation of the tangent line to the curve described by the particle at t = π/4.

(c) (10 points) Find the time(s) (if any) when the particle’s acceleration vector is orthogonal to its velocity vector.

Please show work.