1. Tardigrade
  2. Question
  3. Mathematics
  4. The equation of the plane passing through the point (-1,3,2) and perpendicular to each of the planes x+2 y+3 z=5 and 3 x+3 y+z=0 is a x+b y+c z+25=0, then the value of (a+b+c), 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 point $(-1,3,2)$ and perpendicular to each of the planes $x+2 y+3 z=5$ and $3 x+3 y+z=0$ is $a x+b y+c z+25=0$, then the value of $(a+b+c)$, is

Vector Algebra

Solution:

Equation of the plane through $-1,3,2$, is
$a ( x +1)+ b ( y -3)+ c ( z -2)=0$....(1)
(1) is perpendicular to $3+2 y+3 z=5$ and $3 x+3 y+z=0$
Hence equation of plane is
$7(x+1)-8(y-3)+3(z-2)=0 $
$7 x-8 y+3 z+25=0 \equiv a x+b y+c z+25$
Hence $a + b + c =7-8+3=2$