1. Tardigrade
  2. Question
  3. Mathematics
  4. The equation of the plane that contains the point (1,-1,2) and is perpendicular to each of the planes 2 x+3 y-2 z=5 and x+2 y-3 z=8, is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The equation of the plane that contains the point $(1,-1,2)$ and is perpendicular to each of the planes $2 x+3 y-2 z=5$ and $x+2 y-3 z=8$, is

Three Dimensional Geometry

Solution:

The equation of the plane containing the given point is
$A(x-1)+B(y+1)+C(z-2)=0$...(i)
Applying the condition of perpendicularly to the plane given in Eq. (i) with the planes
$2 x+3 y-2 z =5 \text { and } x+2 y-3 z=8, \text { we have }$
$2 A+3 B-2 C =0 \text { and } A+2 B-3 C=0$
Solving these equations, we find $A=-5 C$ and $B=4 C$.
Hence, the required equation is
$-5 C(x-1)+4 C(y+1)+C(z-2)=0$
i.e., $5 x-4 y-z=7$