Equation of a plane $Ax+By+Cz=D$ I have question abous parametrization and plane equation.How can I write the equation of a plane in the form $Ax+By+Cz=D$ if it is given as
$$x=2s+3t$$
$$y=s-2t$$
$$z=3s+t$$.

You have to explicit $s$ and $t$ from two of the three equations, then substitute in the remaining one. Pratically, explicit $s$ from the second equation
$$s=y+2t$$
so, we get
$$\begin{cases} x=2(y+2t)+3t \\ s=y+2t \\ z=3(y+2t)+t\end{cases}\quad \Longrightarrow \quad \begin{cases} x=2y+7t \\ s=y+2t \\ z=3y+7t \end{cases}.$$
Now, you have to explicit $t$ from the first or the third equation. For example, take $t$ from the first:
$$t=\frac{x-2y}{7}$$
and substitute it in the remaining equation. So you get
$$z=3y+7\frac{x-2y}{7} \quad \Longrightarrow \quad z=3y+x-2y \quad \Longrightarrow \quad x+y-z=0.$$
Finally you are in the form $Ax+By+Cz=D$ where $A=1$, $B=1$, $C=-1$ and $D=0$.
