The angle between x=2 and x-3y=6 is

Correct Answer is : tan⁡−1(3)^{-1}(3)tan−1(3)

Correct Answer is : tan⁡−1(3)^{-1}(3)tan−1(3)

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CGPET 2019 Solved Paper

Section: Mathematics

Question : 143 of 150

Marks: +1, -0

The angle between

x=2

x-3y=6

Solution:

Since,

x=2

is parallel to

Y

-axis.

So, the angle between the line

x=2

and

x-3y=6

is the angle between

x-3y=6

and

Y

-axis which is given by

\tan \theta = \left| \frac{1}{m} \right|

, where

m

is the slope of the line

x-3y=6

Consider the line

x-3y=6,-3y=6-x

\Rightarrow y = \frac{x-6}{3} = \frac{x}{3} - 2

Slope of the line

x-3y=6

\frac{1}{3}

Therefore,

\tan \theta = \left| \frac{1}{\frac{1}{3}} \right| = |3|

\Rightarrow \theta = \tan^{-1}(3)

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