Question

The plane which bisects the line joining the points $(4,-2,3)$ and $(2,4,-1)$ at right angles also passes through the point:

• A. $(0,-1,1)$
• B. $(4,0,1)$
• C. $(4,0,-1)$
• D. $(0,1,-1)$

Answer 1

The correct option is C $(4,0,-1)$


Mid point $P=(3,1,1)$
Normal of plane is along line $AB$
$D.R{.}^{\prime }s$ of normal $=(2,-6,4)$
Equation of plane is
$\Rightarrow 2(x-3)-6(y-1)+4(z-1)=0$
$\Rightarrow x-3y+2z-2=0$
From the given options, the plane passes through the point $(4,0,-1).$