Intersection of line and plane

[Physicsissuef]

Homework Statement

Find the equation of the plane which passes through the line $\frac{x-2}{3}=\frac{y-3}{1}=\frac{z+1}{2}$
and it is normal to the plane x+4yy-3z+7=0

Homework Equations

The Attempt at a Solution

I find the intersection point of the plane and the line. It is M(2,3,-1). Also I got the condition (A,B,C)(3,1,2)=0

$$\left\{\begin{matrix} 2A+3B-C+D=0 & \\ A+4B-3C=0 & \end{matrix}\right.$$

What is the third condition ?

 

[Physicsissuef]

Sorry I must fix something. Up in there is x+4y-3z+7=0, and (A,B,C)(1,4,-3)=0.

 

[Physicsissuef]

Is (A,B,C)(3,1,2)=0 the third condition?