Q. The family of lines making an angle $30{^\circ}$ with the line $\sqrt{3}y = x + 1$ is
A) $x = \lambda$(λ is parameter )
B) $y = - \sqrt{3}x + \lambda$(λ is parameter )
C) $y = \sqrt{3}x + \lambda$
D) None of the above
Explanation
(c)
Slope of given line is $\frac{1}{\sqrt{3}}$ , it’s angle from positive $x$-axis is $30{^\circ}$ . Now, lines making an angle $30{^\circ}$ from it are either $x$-axis $(ie,\ y = 0)$ or makes and angle $60{^\circ}$ with positive $x$-axis $\left( ie,\ y = \sqrt{3}x + \lambda \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.