Question

The angle between the lines $2x+11y-7=0$ and $x+3y+5=0$ is equal to

• A. $ta{n}^{-1}\frac{17}{31}$
• B. $ta{n}^{-1}\frac{11}{35}$
• C. $ta{n}^{-1}\frac{1}{7}$
• D. $ta{n}^{-1}\frac{33}{35}$
• E. $ta{n}^{-1}\frac{7}{33}$

Answer 1

Answer: (C)

Given lines are $2x+11y-7=0$
and $x+3y+5=0$
$\Rightarrow y=-\frac{2}{11}x+\frac{7}{11}$
and $y=-\frac{1}{3}x-\frac{5}{3}$
Their, slopes are
$m_1=-\frac{2}{11}$
and
$m_2=-\frac{1}{3}$
$\therefore$ Angle between lines is
$\tan \theta =\frac{m_1-m_2}{1+m_1{m}_2}$
$=\frac{-\frac{2}{11}+\frac{1}{3}}{1+\frac{2}{11}\times \frac{1}{3}}=\frac{-6+11}{33+2}=\frac{5}{35}$
$\Rightarrow \theta ={\tan }^{-1}\left(\frac{1}{7}\right)$