Question

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+23=0 and 3x−y+1=0 is β. Which one of the following is correct?

• A. (A) α=β
• B. (B) α>β
• C. (C) α<β
• D. (D) α=2β

Answer 1

Answer: (B)

(B) α>β

Answer 2

Explanation:
Given:Angle between the lines x+y−3=0 and x−y+3=0 is α.Angle between the lines x−3y+23=0 and 3x−y+1=0 is β.The angle θ between the lines having slope m1 and m2 is given by tan⁡θ=|m2−m11+m1m2|Let's find the slope,Slope of line x+y−3=0 is m1 and slope of line x−y+3=0 is m2m1=−1 and m2=1Therefore,tan⁡α=|1−(−1)1+(−1)×1|=∞α=90∘Slope of line x−3y+23=0 is m1 and 3x−y+1=0 is m2m1=(13) and m2=3tan⁡β=|3−131+(3×13)|=13β=30∘α>βHence, the correct option is (B).