On a coordinate plane, there are two points $A ( - 3,4 ) , B ( 3,2 )$ and a line $L$. Points $A$ and $B$ are on opposite sides of line $L$, and $\vec { n } = ( 4 , - 3 )$ is a normal vector to line $L$. The distance from point $A$ to line $L$ is 5 times the distance from point $B$ to line $L$. Based on the above, answer the following questions. (1) Find the dot product of vector $\overrightarrow { A B }$ and vector $\vec { n }$. (4 points) (2) Find the equation of line $L$. (4 points) (3) Point $P$ is on line $L$ and $\overline { P A } = \overline { P B }$. Find the coordinates of point $P$. (4 points)
On a coordinate plane, there are two points $A ( - 3,4 ) , B ( 3,2 )$ and a line $L$. Points $A$ and $B$ are on opposite sides of line $L$, and $\vec { n } = ( 4 , - 3 )$ is a normal vector to line $L$. The distance from point $A$ to line $L$ is 5 times the distance from point $B$ to line $L$. Based on the above, answer the following questions.\\
(1) Find the dot product of vector $\overrightarrow { A B }$ and vector $\vec { n }$. (4 points)\\
(2) Find the equation of line $L$. (4 points)\\
(3) Point $P$ is on line $L$ and $\overline { P A } = \overline { P B }$. Find the coordinates of point $P$. (4 points)