Question

The angle between the straight lines $x-y\sqrt{3}=5$ and $\sqrt{3}x+y=7$ is

• (A) 90^o
• (B) 60^o
• (C) 75^o
• (D) 30^o

Answer 1

The Correct Option is A

Explanation:
Given, equations of straight lines are$$x-y\sqrt{3}=5\text{ and }\sqrt{3}x+y=7$$On comparing with $ax+by=0,$ we get$$a_1=1,b_1=-\sqrt{3},a_2=\sqrt{3},b_2=1$$Now, $a_1{a}_2+b_1{b}_2=1\cdot \sqrt{3}+(-\sqrt{3})\cdot 1=0$$\therefore$ Lines are perpendicular.$\therefore$$$\theta ={90}^{\circ }$$