Answer is (A) (−3, 2, 1)
From the given data, we can plot the graph as shown in the following figure:
Plane bisects the line AB perpendicularly. Therefore, the midpoint of AB is
((-3 + 1)/2, (4 + 2)/2, (3 + 5)/2) = (-1, 3, 4)
Now, the direction ratio of AB is (−4, 2, 2).
Therefore, equation of plane is given by
−4(x + 1) + 2(y – 3) + 2(z − 4) = 0
⇒ −4x – 4 + 2y – 6 + 2z – 8 = 0
⇒ −4x + 2y + 2z – 18 = 0
⇒ −2x + y + z = 9
Only (−3, 2, 1) satisfies the plane