Let \(\phi\) be the angle between the two lines.
tan \(\phi\) = \(\frac{m_1 - m_2}{1 + m_1 m_2}\)
where m\(_1\) = slope of line 1; m\(_2\) = slope of line 2.
Line 1: 2x + y = 3 \(\implies\) y = 3 - 2x.
Line 2: 3x - 2y = 5 \(\implies\) -2y = 5 - 3x.
y = \(\frac{3}{2}\)x - \(\frac{5}{2}\).
m\(_1\) = -2, m\(_2\) = \(\frac{3}{2}\).
tan \(\phi\) = \(\frac{-2 - \frac{3}{2}}{1 + (-2 \times \frac{3}{2})}\)
= \(\frac{\frac{-7}{2}}{-2}\)
\(\therefore\) Tan \(\phi\) = \(\frac{7}{4}\).