Question

Angle between$x=2andx-3y=6is$

• A. $\infty$
• B. ${\tan }^{-1}\left(3\right)$
• C. ${\tan }^{-1}\left(\frac{1}{3}\right)$
• D. $noneofthese$

Answer 1

The correct option is B

${\tan }^{-1}\left(3\right)$

Explanation for the correct option:

Finding the angle:

Given,$x=2...\left(\mathrm{i}\right)$

This line is parallel to $y-$axis

$x-3y=6...\left(\mathrm{ii}\right)$

Then angle between them$=-\frac{1}{\mathrm{m}}$

$=\frac{1}{(slopeofthesecondline)}$

If one of the lines is parallel to the $y-$axis then the angle between two straight lines is given by$\tan \theta =\pm \frac{1}{m}$ where $\text{'}m\text{'}$ is the slope of the other straight line.

The angle between these two lines is assumed to be acute and hence, the value of $\tan \left(\theta \right)$ is taken to be positive.

so $\tan \left(\theta \right)=\frac{1}{{\displaystyle \frac{1}{3}}}$

$=3$

$\Rightarrow$$tan\left(\mathrm{\theta }\right)=3$

$\Rightarrow$ $\theta =ta{n}^{-1}\left(3\right)$

Hence, option(B) is correct.