Given the multivariate function $f(x, y, z) = 5x^1z^1 + 2ln(y^2)$ and the point $P = (3,3,2)$, what is the direction in which the function increases most rapidly at the point P?
Give your answer in the form
$\begin{pmatrix} a \ b \ c \end{pmatrix}$, using the formula editor.
The direction is given by