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Find the angle between the lines whose slopes are 1/2 and 3 ?
1. 30° 
2. 60°
3. 90°
4. 45° 
5. None of these

1 Answer

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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.

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