
Lines and planes.
it's given the plane determined 2 equations of lines l1 and l2 and it is given point P(3,4,2) outside the plane find the coordinate of P1 symetric with the plane.
$\displaystyle l_1 : \frac{x5}{13}=\frac{y6}{1}=\frac{z+3}{4}$
$\displaystyle l_2 : \frac{x2}{13}=\frac{y3}{1}=\frac{z+3}{4}$
what i did so far is :
I've found the normal vector of the plane using one vector of the lines and vector M1M2 . M1 is point of line 1 and m2 of l2.
then i found the equation of the plane using this vector and and a point M1 or M2.
then i found the equation of the normal line from point P and the normal vector of the plane.
am i right till here
Now how to find the coordinates of P1??
have i to find the length from P to plane, and the point witch the normal line intersect the plane and then using the same distance i should find P1 from point K( where the normal line intersect the plane).
normal = perpendicular

Now i have an idea (Nod)
we must find the vector from point P to the point of intersection of the normal line with the plane K and then this vector add to the coordinates to the point
K so we found the coordinates P1 ???