Question

A plane bisects the line segment joining the points $(1,2,3)$ and $(-3,4,5)$ at right angles. Then this plane also passes through the point :

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

Answer 1

The correct option is C $(-3,2,1)$

Let M is the mid point of line $AB$ and line $AB$ is the perpendicular to plane


$\therefore$ coordinate of point $M$ is $(-1,3,4)$
Normal vector of the plane, $\overrightarrow{n}=-4\hat{i}+2\hat{j}+2\hat{k}$
Therefore, Equation of plane is
$(x+1)(-4)+(y-3)2+(z-4)2=0$
$\Rightarrow -2x+y+z-9=0$
Clearly, point $(-3,2,1)$ satisfy the above equation.