Question

Assertion :Let $A(i+j+k)$ and $B(i-j+k)$ be two points, then point $P(2i+3j+k)$ is exterior to the sphere with $A$ and $B$ as ends of its diameter Reason: If $A$ and $B$ are any two points and $P$ is a point in space such that $\overline{PA}.\overline{PB}>0$, then the point $P$ lies exterior to the sphere with $AB$ as one of its diameters

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Given that $A(i+j+k)$ and $B(i-j+k)$ are diameters of a sphere

The point $P$ is $(2i+3j+k)$

$PA=i+2j$ and $PB=i+4j$

So we get $PA.PB=(i+2j).(i+4j)=1+8=9>0$

If $A$ and $B$ are two points and $P$ is a point in space such that $PA.PB>0$ , then the point $P$ lies exterior to the sphere with $AB$ as one of its diameter

Therefore assertion is correct and reason is correct explanation if assertion

Therefore option $A$ is correct