Question

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

• A. 2
• B. 4
• C. 12
• D. 18

Answer 1

Answer: (A)

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