Determine whether the following statements are true and give an explanation or counterexample. 

a. The vectors r(t) and r'(t) are parallel for all values of t in the
domain.
b. The curve described by the function r(t) = (t, t² - 2t, cos πt)
is smooth, for -∞ < t < ∞.
c. If f, g, and h are odd integrable functions and a is a real number, then

Transcribed Image Text:

(f(1) i + g(t) j + h(t) k) dt = 0. 0. p-