Q. A straight line through the point (2, 2) intersects the lines $\sqrt{3}x + y = 0$ and $\sqrt{3}x - y = 0$ at the point $A$ and $B$. The equation to the line $AB$ so that the $\mathrm{\Delta}\ OAB$ is equilateral is
A) $x - 2 = 0$
B) $y - 2 = 0$
C) $x + y - 4 = 0$
D) None of these
Explanation
(b)
$\sqrt{3}x + y = 0$ makes an angle of $120{^\circ}$ with $OX$ and $\sqrt{3}x - y = 0$ makes an angle $60{^\circ}$ with $OX$. So, the required line is $y - 2 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.