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 \(\phi\) = \(\frac{7}{4}\).