Question

The angle between the lines $y=(2-\sqrt{3})x+7$ and $y=(2+\sqrt{3})x-3$ is:

• A. ${30}^o$
• B. ${60}^o$
• C. ${45}^o$
• D. ${90}^o$

Answer 1

Answer: (B)

${60}^o$

Let the slope of first line be $m_1$ and slope of the 2nd line be $m_2.$

On comparing the given equations with the standard form $y=mx+c$

$m_1=2-\sqrt{3}$

$m_2=2+\sqrt{3}$

Let $\theta$ be angle between lines.

As we know, $\tan \theta$ between line with slopes $m_1$ and $m_2$ is determined by$:-$

$\tan \theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|$

$\Rightarrow \tan \theta =\left|\frac{2-\sqrt{3}-(2+\sqrt{3})}{1+(2-\sqrt{3})(2+\sqrt{3})}\right|$

$\Rightarrow \tan \theta =\left|\frac{-2\sqrt{3}}{2}\right|$

$\Rightarrow \tan \theta =|-\sqrt{3}|$

$\therefore \tan \theta =\sqrt{3}$

$\therefore \theta ={60}^{\circ }$