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Subhash Akhil Ganguly
Asked: 2022-11-09T16:30:17+05:30 In:

What is the acute angle between the pair of straight lines 2x + y = 1 and 3x – y = 2
1. \(\rm tan^{-1} 1\)
2. \(\rm tan^{-1}(\frac{4}{7})\)
3. \(\rm tan^{-1}(\frac{2}{3})\)
4. \(\rm tan^{-1}(\frac{4}{3})\)

What is the acute angle between the pair of straight lines 2x + y = 1 and 3x – y = 2
1. \(\rm tan^{-1} 1\)
2. \(\rm tan^{-1}(\frac{4}{7})\)
3. \(\rm tan^{-1}(\frac{2}{3})\)
4. \(\rm tan^{-1}(\frac{4}{3})\)
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  1. Correct Answer – Option 1 : \(\rm tan^{-1} 1\)

    Concept:

    Angle between two lines is given by, \(\rm \theta =tan^{-1}|\frac{m_2-m_1}{1+m_1m_2}|\), m1 and m2 are slopes of lines.

    Equatin of straight line: y = mx + c, where m =slope

     

    Calculation:

    Here, the pair of straight lines are 2x + y = 1 and 3x – y = 2

    2x + y = 1 ⇒y = -2x + 1 so, m1 = -2

    And, 3x – y = 2 ⇒y = 3x – 2 so, m2 = 3

    So, angle between given pair of straight lines = \(\rm \theta =tan^{-1}|\frac{m_2-m_1}{1+m_1m_2}|\)

     \(\rm =tan^{-1}|\frac{3-(-2)}{1+3(-2)}|\\ =tan^{-1} 1\)

    Hence, option (1) is correct. 

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