Embibe Experts Solutions for Chapter: Point and Straight Line, Exercise 1: JEE Advanced Paper 1 - 2014

Let $O$ be the origin and let $PQR$ be an arbitrary triangle. The point$S$ is such that $\overrightarrow{OP}.\overrightarrow{OQ}+\overrightarrow{OR}.\overrightarrow{OS}=\overrightarrow{OR}.\overrightarrow{OP}+\overrightarrow{OQ}.\overrightarrow{OS}=\overrightarrow{OQ}.\overrightarrow{OR}+\overrightarrow{OP}.\overrightarrow{OS}$ then triangle $PQR$ has $S$ as its

For $a>b>c>0$, the distance between $(1,1)$ and the point of intersection of the lines $ax+by+c=0$ and $bx+ay+c=0$ is less than $2\sqrt{2}$. Then