Let $$f(x, y) = x^2+\sin(xy), \quad x(t) = 3 t+6, \quad \text{and}\quad y(t) = 3 t^2+8 t.$$ The parametric curve $\mathbf{c}(t) = ( x(t), y(t), f( x(t), y(t) ) )$ lies on the surface $z = f(x,y)$. Find the tangent vector to this curve at $t = 1$.

Tangent vector $=($ , , $)$