Let curve C be the curve

r(t) = (4(sin t t cos t), 4(cos t + t sin t), 3/2t²), for t 0.

a. Write the length of the arc s (as a function of t) measured from the point P(0, 4, 0) and with the same orientation as the original curve.

b. Find the arc-length parametrization r(s) of C.

c. Find the coordinates of the point on the curve that is 10 units away from P in the direction of the increasing parameter.