Sketch the curve represented by the vector-valued function

Question

1. Sketch the curve represented by the vector-valued function and give the orientation of the curve r(t) = 2sin ti + tj + 3cos tk.

2. For the vector-valued function r(t) = (sin t - t cos t)i + (cos t + t sin t)j + (t)k, find

i. r' (t)
ii. r'' (t)
iii. r' (t) · r'' (t).

3. For the vector-valued function r(t) = (ln t)i + (2 sin t cos t)j + (4/t³) k find

i. r' (t)

ii. ∫ r(t)dt