Question

The equation of the plane, which bisects the line joining the points $(1,2,3)$ and $(3,4,5)$ at right angles is,

• A. $x+y+z=0$
• B. $x+y-z=9$
• C. $x+y+z=9$
• D. $x+y-z+9=0$

Answer 1

The correct option is C $x+y+z=9$

To get equation of plane, it is sufficient to know one point on the plane and direction ratio of normal to the plane.

Direction ratio of normal to plane is direction ratio of line joining the given $2$ points
$(3-1)\hat{i}+(4-2)\hat{j}+(5-3)\hat{k}$

A point on plane is midpoint of given two points
$(\frac{1+3}{2},\frac{2+4}{2},\frac{3+5}{2})$

Equation of required plane is $2(x-2)+2(y-3)+2(z-4)=0$
Equation of plane is $x+y+z=9$