NDA 2016 Maths · Mathematics · Straight Lines · hard

The acute angle between the lines y=√3 x+1 and y=(x)/(√3)-2 is

Single correct option

The acute angle between the lines

y=\sqrt3\,x+1

and

y=\dfrac{x}{\sqrt3}-2

Show answer and solution

Answer: (A) $30^\circ$

The slopes are

m_1=\sqrt3

and

m_2=1/\sqrt3

\tan\theta=\left|\dfrac{m_1-m_2}{1+m_1m_2}\right|=\dfrac{2/\sqrt3}{2}=\dfrac1{\sqrt3}

, so

\theta=30^\circ

. The lines make

60^\circ

and

30^\circ

with the x-axis, so the angle between them is their difference.

Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake