On the coordinate plane, two parallel lines $L _ { 1 } , L _ { 2 }$ both have slope 2 and are at distance 5 apart. Point $A ( 2 , - 1 )$ is a point on $L _ { 1 }$ in the fourth quadrant. Point $B$ is a point on $L _ { 2 }$ in the second quadrant with $\overline { A B } = 5$ . Line $L _ { 3 }$ has slope 3, passes through point $A$, and intersects $L _ { 2 }$ at point $C$. Answer the following questions: (1) Find the slope of line $AB$ . (2 points) (2) Find the vector $\overrightarrow { A B }$ . (4 points) (3) Find the dot product $\overrightarrow { A B } \cdot \overrightarrow { A C }$ . (3 points) (4) Find the vector $\overrightarrow { A C }$ . (4 points)
On the coordinate plane, two parallel lines $L _ { 1 } , L _ { 2 }$ both have slope 2 and are at distance 5 apart. Point $A ( 2 , - 1 )$ is a point on $L _ { 1 }$ in the fourth quadrant. Point $B$ is a point on $L _ { 2 }$ in the second quadrant with $\overline { A B } = 5$ . Line $L _ { 3 }$ has slope 3, passes through point $A$, and intersects $L _ { 2 }$ at point $C$. Answer the following questions:\\
(1) Find the slope of line $AB$ . (2 points)\\
(2) Find the vector $\overrightarrow { A B }$ . (4 points)\\
(3) Find the dot product $\overrightarrow { A B } \cdot \overrightarrow { A C }$ . (3 points)\\
(4) Find the vector $\overrightarrow { A C }$ . (4 points)