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The equation of the right bisecting plane of line segment joining the points $A \equiv (a, a, 2 a)$ and $B \equiv (- a, - a, a)$ is

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$x + y + z = a$

$4 x + 2 y + z = 3 a$

$4 x - 2 y + z = 3 a$

$4 x + 4 y + z = 3 a$

answer is D.

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Detailed Solution

Mid-point of $A B = (0, 0, 3 a / 2)$ and D.R.’s of $A B$ are $(2 a, 2 a, a)$

$∴$ Equation of right bisecting plane of $A B$ is $2 a (x - 0) + 2 a (y - 0) + a (z - 3 a / 2) = 0$

$\Rightarrow 4 x + 4 y + 2 z = 3 a$ .

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