Q) Find the angle between the pair of straight lines:

x – 4 y = 3 and 6 x – y = 11.

[Practice Paper 1, 2023-24, Dir of Edu, GNCT of Delhi]

Ans: 

The equations of the lines are x – 4y = 3 and 6 x – y = 11

Let’s rewrite these equations in standard form (y = m x + c), we get:

x – 4 y = 3

∴ x – 3 = 4 y

∴ y = …… (i)

Similarly, 6 x – y = 11

∴ y = 6 x – 11 …. (ii)

Comparing these lines with standard equation: y = m x + c, we get:

Slope of 1^st line, m₁ =

and slope of 2^nd line, m₂ = 6

Next, let’s consider the angle between these 2 lines is θ

We know that the angle between two lines of slope m₁ and m₂ is calculated by:

tan θ =

*** QuickLaTeX cannot compile formula:
\mod{

*** Error message:
File ended while scanning use of \mod.
Emergency stop.

\frac{m_1 – m_2}{1 + m_1 m_2}}\mod{\frac{\frac{1}{4} – 6}{1 + (\frac{1}{4}) (6)}}\mod{\frac{{\frac{- 23}{4}}{1 + \frac{6}{4}}}\mod{\frac{{\frac{- 23}{4}}{\frac{10}{4}}}\mod{\frac{- 23}{10}}\frac{- 23}{10}\tan^{- 1} \frac{- 23}{10}\tan^{- 1} \frac{- 23}{10}$

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