I am trying to plot a plane such that the yaxis is constant at 3 on a 3D graph. So the plane is going to be stick upwards parrellel to xaxis while staying at y=3 throughout. The idea is to actually have this plane to cut another surface. I try to get the function in the form of z=f(x,y) and here's what I did:
Since the plane is a constant y=3 plane, I assume (0, 3, 0) is a point on the plane. Then I move 5 in the zaxis and then minus them to get a vector direction.
$\displaystyle \begin{pmatrix}
0\\
3\\
0
\end{pmatrix}

\begin{pmatrix}
5\\
3\\
0
\end{pmatrix}
=
\begin{pmatrix}
5\\
0\\
0
\end{pmatrix}
$
I then get another vector direction on this plane by moving 2steps up zaxis and 5 steps to xaxis; (2, 3, 5).
$\displaystyle
\begin{pmatrix}
0\\
3\\
0
\end{pmatrix}

\begin{pmatrix}
2\\
3\\
5
\end{pmatrix}
=
\begin{pmatrix}
2\\
0\\
5
\end{pmatrix}
$
Then I cross these 2 direction vectors to get the normal line.
$\displaystyle
\begin{pmatrix}
5\\
0\\
0
\end{pmatrix}
\times
\begin{pmatrix}
2\\
0\\
5
\end{pmatrix}
=
\begin{pmatrix}
0\\
25\\
0
\end{pmatrix}
$
I then did a dot product of this normal vector with the point (0, 3, 0) to get the equation of the plane: $\displaystyle 0x 25y +0z = 75$
But, from $\displaystyle 0x 25y +0z = 75$, how do I form it to z=f(x, y)? z is zero in this case and I can't make it the subject in terms of x and y.
How should I carry on from here? Thanks.