Q. The angle between the straight line $x - y\sqrt{3} = 5$ and $\sqrt{3}x + y = 7$ is
A) $90{^\circ}$
B) $60{^\circ}$
C) $75{^\circ}$
D) $30{^\circ}$
Explanation
(a)
Given equation is compared with $a_{1}x + b_{1}y = 0$ and $a_{2}x + b_{2}y = 0$
Now, $a_{1}a_{2} + b_{1}b_{2} = (1)\left( \sqrt{3} \right) + \left( - \sqrt{3} \right)(1) = 0$
$\therefore$ Lines are perpendicular
Hence, $\theta = 90{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.