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BITSAT 2023Paper 1
Exam
BITSAT
Year
2023
Paper
Paper 1
Subject
Mathematics
Chapter
Straight Lines

BITSAT 2023 · Paper 1 · Mathematics · Straight Lines

What is the angle between the two straight lines y=(2- 3 ) x+5 and...

What is the angle between the two straight lines y=(2−3)x+5y=(2-\sqrt{3}) x+5 and y=(2+3)x−7?y=(2+\sqrt{3}) x-7 ?

Options

  1. A60∘60^{{}^{\circ}}
  2. B45∘45^{{}^{\circ}}
  3. C30∘30^{{}^{\circ}}
  4. D15∘15^{{}^{\circ}}

Correct answer

A. 60∘60^{{}^{\circ}}

Step-by-step solution

The given lines are:
y=(2−3)x+5 and y=(2+3)x−7y=(2-\sqrt{3}) x+5 \text{ and } y=(2+\sqrt{3}) x-7
Therefore, slope of first line =m1=2−3=m_1=2-\sqrt{3} and slope of second line =m2=2+3=m_2=2+\sqrt{3}
∴tan⁡θ=∣m2−m11+m1m2∣=∣2+3−2+31+(4−3)∣\therefore \quad \tan \theta=\left|\frac{m_2-m_1}{1+m_1 m_2}\right|=\left|\frac{2+\sqrt{3}-2+\sqrt{3}}{1+(4-3)}\right|
=∣232∣=3=tan⁡π3⇒θ=π3=60∘=\left|\frac{2 \sqrt{3}}{2}\right|=\sqrt{3}=\tan \frac{\pi}{3} \Rightarrow \theta=\frac{\pi}{3}=60^{{}^{\circ}}
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