A particle moves along a curve r(t) from time t = 0 to time t = 12. The particle's position at time t is given by the equation r(t) = cos(t/2)i + tj sin(t/2) k, with i = (1, 0, 0), j = (0, 1, 0) and k = (0, 0, 1) the Cartesian basis vectors of R³ .

1) Sketch the particle trajectory from t = 0 to t = 12, as a 2D projection onto the xz-plane.

2) Describe, in words, the shape of the 3D curve r(t).

3) Calculate the arc length of the curve from t = 0 to t = 12.