Coordinate Geometry

Mathematics (NDA)

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The angle between the lines x + y − 3 = 0 and x − y + 3 = 0 is α and the acute angle between the lines x − √3y + 2√3 = 0 and √3x − y + 1 = 0 is β. Which one of the following is correct?

α = β

α > β

α < β

α = 2β

Explanation:

cos α = 1−1−9 / √1+1+9√1+1+9 = -9/11

Implies that α lies in 2nd or 3rd quadrant.

Cos β = √3+√3+2√3 / √1+3+12√3+1+1 = 4√3 / √5√16 = √3 / √5

Implies that β lies in 1st or 4th quadrant. Therefore α > β.

By: Yachna

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