Question

Find the angle between the lines joining the points $(0,0),(2,3)$ and $(2,-2),(3,5)$.

Answer 1

slope of line L1 = $\frac{3-0}{2-0}=\frac{3}{2}$

slope of line L2 = $\frac{5+2}{3-2}=7$

Angle between $L_1,L_2=ta{n}^{-1}\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|=ta{n}^{-1}\left|\frac{\frac{3}{2}-7}{1+\frac{3}{2}\left(7\right)}\right|$

$=ta{n}^{-1}\frac{11/2}{23/2}=ta{n}^{-1}\frac{11}{23}$