SATHEE: Straight Line Question 219

Straight Line Question 219

Question: What is the acute angle between the lines represented by the equations $ y-\sqrt{3}x-5=0 $ and $ \sqrt{3}x-x+6=0? $

Options:

A) $ 30{}^\circ $

B) $ 45{}^\circ $

C) $ 60{}^\circ $

D) $ 75{}^\circ $

Show Answer

Answer:

Correct Answer: A

Solution:

[a] $ y-\sqrt{3}x-5=0 $ line one $ \sqrt{3}y-x+6=0 $ Line two $ y=mx+c $ $ y=\sqrt{3}x+5 $$ y=\frac{x}{\sqrt{3}}-\frac{6}{\sqrt{3}} $ $ m_1=\sqrt{3} $ $ m_2=\frac{1}{\sqrt{3}} $ Angle between two lines, $ \tan \theta =| \frac{m_1-m_2}{1+m_1m_2} | $ $ =| \frac{\sqrt{3}-\frac{1}{\sqrt{3}}}{1+\sqrt{3}\frac{1}{\sqrt{3}}} |=\frac{1}{\sqrt{3}} $ $ =\tan 30{}^\circ $

$ \therefore \theta =30{}^\circ $

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Straight Line Question 219

Question: What is the acute angle between the lines represented by the equations $ y-\sqrt{3}x-5=0 $ and $ \sqrt{3}x-x+6=0? $

Options:

Answer:

Solution:

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