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)
Here, $a_{1} = 1,\ b_{1} = - \sqrt{3},\ a_{2} = \sqrt{3},\ b_{2} = 1$
Now, $a_{1}a_{2} + b_{1}b_{2} = 1 \bullet \sqrt{3} + \left( - \sqrt{3} \right) \bullet 1 = 0$
$\therefore\$Lines are perpendicular, $ie,\ \theta = 90{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.