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Question

Angle betweenx=2andx-3y=6is


A

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B

tan-1(3)

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C

tan-1(13)

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D

noneofthese

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Solution

The correct option is B

tan-1(3)


Explanation for the correct option:

Finding the angle:

Given,x=2...(i)

This line is parallel to y-axis

x-3y=6...(ii)

Then angle between them=-1m

=1(slopeofthesecondline)

If one of the lines is parallel to the y-axis then the angle between two straight lines is given bytanθ=±1m where 'm' is the slope of the other straight line.

The angle between these two lines is assumed to be acute and hence, the value of tanθ is taken to be positive.

so tanθ=113

=3

tan(θ)=3

θ=tan-1(3)

Hence, option(B) is correct.


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