# Find the angle between the lines whose slope are $\large\frac{3}{2}$ and 7?

$\begin{array}{1 1}(a)\;\theta=\tan^{-1}\large\frac{11}{24}&(b)\;\theta=\tan^{-1}\large\frac{11}{23}\\(c)\;\theta=\tan^{-1}\large\frac{12}{23}&(d)\;\theta=\tan^{-1}\large\frac{10}{23}\end{array}$

$\tan \theta=\bigg| \large\frac{m_1+m_2}{1+m_1m_2}\bigg|$
$\qquad=\bigg|\large\frac{7-\Large\frac{3}{2}}{1+\Large\frac{7\times 3}{2}}\bigg|$
$\tan \theta=\bigg|\large\frac{11}{23}\bigg|$
$\theta=\tan^{-1}\large\frac{11}{23}$
Hence (b) is the correct option.