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
• 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 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

$\frac{x-3}{1}=\frac{y-1}{-1}=\frac{z-6}{1}=\frac{-2(3-1+6-5)}{1+1+1}=-2$

$⟹x=3-2=1$

$\therefore y=1+2=3$

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.