Q$.34$ Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.

$r(t)=3ti+(\frac{2}{3})t^{\frac{3}{2}}k,0t27$

The curve's unit tangent vector is $$ i $+)j+$ k$.$

$($Type exact answers, using radicals as needed.$)$

The length of the indicated portion of the curve is $$ units.

$($Type an integer or a simplified fraction.$)$