The angle between the lines \(2 x+11 y-7=0\) and \(x+3 y+5=0\) is
The angle between the lines \(2 x+11 y-7=0\) and \(x+3 y+5=0\) is
- \(\tan ^{-1}\left(\frac{17}{13}\right)\)
- \(\tan ^{-1}\left(\frac{4}{35}\right)\)
- \(\tan ^{-1}\left(\frac{1}{7}\right)\)
- \(\tan ^{-1}(7)\)
Solution
Given lines \(2 x+11 y-7=0\)
\(\begin{gathered}
\text{and } x+3 y+5=0 \\
m_1=-\frac{2}{11}, m_2=-\frac{1}{3} \\
\tan \theta=\left|\frac{m_1-m_2}{1+m_1 m_2}\right|=\frac{1}{7} \\
\theta=\tan ^{-1}\left(\frac{1}{7}\right)
\end{gathered}\)
Asked in: AP EAMCET 2020 (17 Sep Shift 1)
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