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Assertion :Let A(i+j+k) and B(ij+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 ¯¯¯¯¯¯¯¯PA.¯¯¯¯¯¯¯¯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
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Both Assertion and Reason are incorrect
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Solution

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(ij+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

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