Assertion :Equation of the locus of all those points in space which are equidistant from $x + y + z = 3$ & $x + y + z = 9$ is $x + y + z = 6$ . Reason: If two distinct planes in space are not intersecting then all those points which are equidistant from these planes will lie on a unique plane.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
Planes $x + y + z = 3$ and $x + y + z = 9$ are parallel
Locus of points equidistant from planes will be given by plane,
$x + y + z = \frac{9 + 3}{2}$
$x + y + z = 6$
Assertion is correct.

If two distinct planes are not Intersecting then locus of point equidistant from planes will be a unique plane,between two planes,
reason is also correct,
But it is not stating for parallel planes ,about Assertion ,
Therefore,
option (B) is correct.

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Assertion :Equation of the locus of all those points in space which are equidistant from x+y+z=3 & x+y+z=9 is x+y+z=6. Reason: If two distinct planes in space are not intersecting then all those points which are equidistant from these planes will lie on a unique plane.

Assertion :Equation of the locus of all those points in space which are equidistant from $x + y + z = 3$ & $x + y + z = 9$ is $x + y + z = 6$ . Reason: If two distinct planes in space are not intersecting then all those points which are equidistant from these planes will lie on a unique plane.