Question

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

• A. $(4,1,7)$
• B. $(4,1,-2)$
• C. $(2,3,5)$
• D. $(2,1,3)$

Answer 1

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

$C(0,2,5)$ will be the midpoint of line segment $AB$
drs of normal of required plane $\Rightarrow \overrightarrow{n}=\overrightarrow{B}-\overrightarrow{C}=3\hat{i}+5\hat{j}+\hat{k}$

Equation of required plane
$p:3(x-0)+5(y-2)+1(z-5)=0$

$\therefore 3x+5y+z=15$