Question

$P(0,5,6),Q(1,4,7),R(2,3,7)$ and $S(3,4,6)$ are four points in the space. The point nearest to the origin $O(0,0,0)$ is

• A. only $P$
• B. only $Q$
• C. $R$ and $S$
• D. $P$ and $S$

Answer 1

The correct option is D $P$ and $S$

We have

${OP}^2=0^2+5^2+6^2=0+25+36=61$

${OQ}^2=1^2+4^2+7^2=1+16+49=66$

${OR}^2=2^2+3^2+7^2=4+9+49=62$

${OS}^2=3^2+4^2+6^2=9+16+36=61$

So, $P$ and $S$ are equidistant from O and the nearest to it.