Finding the directional derivative parallel to an intersection of planes We must find the directional derivative of $ f(x,y,z) = x^2 + 2xyz -y^2 $ at $ (1,1,2) $ in a direction parallel to the straight line $ \frac{x-1}{2} = y-1 = \frac{z-2}{-3} $ 
The straight line is an intersection of 2 planes but in 3 variables, how do I write this in the form of a vector so I can find the directional derivative?

The direction vector of the line is $(2, 1, -3)$, the denominators of the three parts.
The parameterised form of the line is
$$x=1+2t, y=1+t, z=2-3t$$
which is 
$$\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}1\\1\\2\end{pmatrix}+t\begin{pmatrix}2\\1\\-3\end{pmatrix}$$
