Correct Answer - Option 4 : (4, 1, -2)
From question, let’s assume the points, A(-3, -3, 4) and B(3, 7, 6).
The midpoint of A and B is:
\(⇒ P\left( {\frac{{ - 3 + 3}}{2},\frac{{ - 3 + 7}}{2},\frac{{4 + 6}}{2}} \right) = P\left( {0,2,5} \right)\)
The required plane is perpendicular bisector of line joining A and B. So direction ratios of normal to the plane is proportional to the direction ratios of line joining A and B.
The direction ratios of AB is:
⇒ 3 + 3, 7 + 3, 6 - 4
⇒ 6, 10, 2
The equation of plane is given by the formula:
a(x - x1) + b(y - y1) + c(z - z1) = 0
On substituting point ‘P’,
⇒ 6(x - 0) + 10(y - 2) + 2(z - 5) = 0
[∴ p(0, 2, 5) line on the plane]
∴ 3x + 5y - 10 + z - 5 = 0
⇒ 3x + 5y + z = 15
On checking all the options,
The point (4, 1, -2) in option (d) satisfies the above equation. So, option (d) is the correct answer.