Question

The angle between the straight lines $x-y\sqrt{3}=5$ and $x\sqrt{3}+y=7$ is

• A. ${60}^{°}$
• B. ${90}^{°}$
• C. ${30}^{°}$
• D. ${75}^{°}$

Answer 1

The correct option is B

${90}^{°}$

Explanation for the correct option:

Given equation of lines are

$x-y\sqrt{3}=5$ and $x\sqrt{3}+y=7$

Slope of the given lines

$m_1=\frac{1}{\sqrt{3}},m_2=-\sqrt{3}$

We know that angle between two lines is given by

$$\begin{gathered} \tan \theta =\left|\frac{m_2-m_1}{1+m_1{m}_2}\right| \\ \Rightarrow \tan \theta =\left|\frac{-\sqrt{3}-{\displaystyle \frac{1}{\sqrt{3}}}}{1+(-\sqrt{3}).\frac{1}{\sqrt{3}}}\right| \\ \Rightarrow \tan \theta =\left|\frac{-4}{0}\right| \\ \Rightarrow \theta ={90}^{°} \end{gathered}$$

Hence, option (B) is the correct answer.