1. Tardigrade
  2. Question
  3. Mathematics
  4. 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

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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

Bihar CECEBihar CECE 2007

Solution:

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.