Correct Answer - Option 4 : 45°
CONCEPT:
If α is the acute angle between two non-vertical and non-perpendicular lines L1 and L2 with slopes m1 and m2 respectively then \(\tan α = \left| {\frac{{{m_2} - {m_1}}}{{1 + {m_1} \cdot {m_2}}}} \right|\)
CALCULATION:
Here, we have to find the angle between the lines whose slopes are 1/2 and 3
Let m1 = 1/2 and m2 = 3
As we know that, \(\tan α = \left| {\frac{{{m_2} - {m_1}}}{{1 + {m_1} \cdot {m_2}}}} \right|\)
⇒ \(\tan α = \left| {\frac{{{3} - {\frac{1}{2}}}}{{1 + {\frac{1}{2}} \cdot {3}}}} \right| = 1\)
⇒ α = 45°
So, the angle between the lines whose slopes are 1/2 and 3 is 45°
Hence, option D is the correct answer.