What is the acute angle between the pair of straight lines 2x + y = 1

1.	What is the acute angle between the pair of straight lines 2x + y = 1 and 3x - y = 21. \(\rm tan^{-1} 1\)2. \(\rm tan^{-1}(\frac{4}{7})\)3. \(\rm tan^{-1}(\frac{2}{3})\)4. \(\rm tan^{-1}(\frac{4}{3})\)
Answer» 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.

What is the acute angle between the pair of straight lines 2x + y = 1 and 3x - y = 21. \(\rm tan^{-1} 1\)2. \(\rm tan^{-1}(\frac{4}{7})\)3. \(\rm tan^{-1}(\frac{2}{3})\)4. \(\rm tan^{-1}(\frac{4}{3})\)

Answer» 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.