Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.\\
$r(t) = 4ti + \left(\frac{2}{3}\right)t^{3/2}k$, $0 \le t \le 33$\
The curve's unit tangent vector is $(oxed{\ })i + (oxed{\ })j + (oxed{\ })k$.\
(Type exact answers, using radicals as needed.)