Question

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

• A. $ta{n}^{-1}\left(\frac{17}{13}\right)$
• B. $ta{n}^{-1}\left(\frac{11}{35}\right)$
• C. $ta{n}^{-1}\left(\frac{1}{7}\right)$
• D. $ta{n}^{-1}\left(\frac{33}{35}\right)$

Answer 1

Answer: (C)

Let $\theta$ be the angle between the two lines
$\therefore tan\theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|$
where $m_1$ and $m_2$ are slopes of given lines.
$2x+11y-7=0$ and $x+3y+5=0$
$\therefore m_1=-\frac{2}{11},m_2=\frac{-1}{3}$

$\therefore tan\theta =\left|\frac{-\frac{1}{3}+\frac{2}{11}}{1+\left(\frac{-2}{11}\times \frac{-1}{3}\right)}\right|=\left|\frac{-11+6}{33+2}\right|$

$=\left|\frac{-5}{35}\right|=\frac{1}{7}$

$\Rightarrow \theta =ta{n}^{-1}\left(\frac{1}{7}\right)$