If we have to find the equation of the plane determined with two lines for example

$\displaystyle l_1 : \frac{x-5}{13}=\frac{y-6}{1}=\frac{z+3}{-4}$

$\displaystyle l_2 : \frac{x +3}{6}=\frac{y+2}{7}=\frac{z-4}{-3}$

and also we know that the lines intersect in a point K.

the normal vector of the plane we find using cross product of vectors from lines.

we find the eqution using this formula $\displaystyle A(x-x_0)+B(y-y_0)+C(z-z_0)=0$

it is wrong to take $\displaystyle M(x_0,y_0,z_0)$ the point of $\displaystyle l_1$ or $\displaystyle l_2$?

should we take the point $\displaystyle K$ as $\displaystyle M(x_0,y_0,z_0)$??

and can someone explain if we take different points of the plane to find the equation we get different equations but it's still the same plane, should we write the equations in normal form?

thanks for any reply!