The equation of the plane that perpendicularly bisects the line segment joining the points A ( 2 , − 1 , 3 ) and B ( 3 , 1 , 0 ) is:

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The plane perpendicularly bisects the line segment joining $A (2, - 1, 3)$ and $B (3, 1, 0)$ .

The plane passes through the midpoint of $A B$ .

Midpoint $M = (\frac{2 + 3}{2}, \frac{- 1 + 1}{2}, \frac{3 + 0}{2}) = (\frac{5}{2}, 0, \frac{3}{2})$

The normal to the plane is parallel to the line segment $A B$ .

Direction ratios of the normal $n = (3 - 2, 1 - (- 1), 0 - 3) = (1, 2, - 3)$

The equation of the plane passing through $M$ with normal $n$ is:

$1 (x - \frac{5}{2}) + 2 (y - 0) - 3 (z - \frac{3}{2}) = 0$

$x - \frac{5}{2} + 2 y - 3 z + \frac{9}{2} = 0$

$x + 2 y - 3 z + \frac{4}{2} = 0$

$x + 2 y - 3 z + 2 = 0$

Answer: $x + 2 y - 3 z + 2 = 0$

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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