Question

The equation of the plane passing through the mid point of the line of join of the points $(1, 2, 3)$ and $(3, 4, 5)$ and perpendicular to it is

• A. $x+y+z=9$
• B. $x+y+z=-9$
• C. $2x+3y+4z=9$
• D. $2x+3y+4z=-9$

Answer 1

Answer: (A)

$x+y+z=9$

Answer 2

The DR's of the joining of the points $(1,2,3)$ and $(3,4,5)$ are $(3-1,4-2,5-3)$, i.e., $(2,2,2)$
Also, the mid point of the join of the points $(1,2,3)$ and $(3,4,5)$ is $(2,3,4)$
$\therefore$ Equation of plane which passes through $(2,3,4)$ and the D.R.'s of its normal are $(2,2)$ is
$2(x-2)+2(y-3)+2(z-4)=0$
$\Rightarrow x+y+z-9=0$
$\Rightarrow x+y+z=9 .$
Note : If any line is perpendicular to the plane then the DR's of a line is equal to the DR's of the normal to the plane.