Write a in the form a = a_\text{T}T + a_\text{N}N at the given value of t without finding T and N.
r(t) = (3e^t \sin t)\mathbf{i} + (3e^t \sqrt{3})\mathbf{j} + (3e^t \cos t)\mathbf{k}, \quad t = 0
a(0) = \boxed{}\mathbf{T} + \boxed{}\mathbf{N}
(Type exact answers, using radicals as needed.)