InterviewSolution
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InterviewSolution
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Find angles between the lines `sqrt(3)x+y=1`and `x+sqrt(3)y=1`. |
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Answer» `sqrt3x+y=1 Rightarrow y=-sqrt3x+1` and `x+sqrt3y=1 Rightarrow y=-(1)/(sqrt3)x+(1)/(sqrt3)` `therefore m_(1)=-sqrt3 and m_(2)=(-1)/(sqrt3)` Let `theta` the angle between the given lines. Then, `tan theta=|(m_(2)-m_(1))/(1+m_(1)m_(2))|=|((-1)/(sqrt3)+sqrt3)/({1+(-sqrt3)xx((-1)/(sqrt3))})|=|(2)/(sqrt3)xx(1)/(2)|=|(1)/(sqrt3)|=(1)/(sqrt3)` `Rightarrow theta=30^(@) and (180^(@)-theta)=(180^(@)-30^(@))=150^(@)` Hence, the angles between the given lines are `30^(@) and 150^(@)` |
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