Question

The plane which bisects the line segment joining the points $(-3,-3,4)$ and $(3,7,6)$ at right angles, passes through which of the following points:

• A. $(2,1,3)$
• B. $(4,-1,2)$
• C. $(4,1,-2)$
• D. $(-2,3,5)$

Answer 1

The correct option is C $(4,1,-2)$

The mid point of the given points $(-3,-3,4)$ and $(3,7,6)$ is $(0,2,5)$ which lies on the plane.
The $D.R^{\prime }s$ of the normal of the plane is $(6,10,2)$
Hence, equation of the plane is $6(x-0)+10(y-2)+2(z-5)=0$
$\Rightarrow 6x+10y+2z=30$
$\Rightarrow 3x+5y+z=15$
Hence, we can observe that only $(4,1,-2)$ lies on the plane.