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Question

Assertion :The point $$A(3, 1, 6)$$ is the mirror image of the point $$B(1, 3, 4)$$ in the plane $$x- y+ z= 5$$ Reason: The plane $$x- y+ z= 5$$ bisects the line segment joining $$A(3, 1, 6)$$ and $$B(1, 3, 4)$$


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 B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
The image of the point (3,1,6) with respect to the plane $$x-y+z=5$$ is 
$$\cfrac{x-3}{1}=\cfrac{y-1}{-1}=\dfrac{z-6}{1}=\cfrac{-2(3-1+6-5)}{1+1+1}=-2$$
$$\Longrightarrow x=3-2=1$$
$$\therefore y=1+2=3$$
and $$ z=6-2=4$$
Which shows that Assertion is true.

We observe that the line segment joining the points $$A(3,1,6)$$ and $$B(1,3,4)$$ has direction ratios  $$2,-2,2 $$ which is proportional to $$(1,-1, 1)$$, the direction ratios of the normal to the plane.
Hence, the reason is true.
Thus, the Assertion and Reason are true and Reason is correct explanation of Assertion.

Mathematics

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