# Math Help - More Planes

1. ## More Planes

Find an equation of a plane that is perpendicular to the plane x-2y+z=7

I know his has to do with vectors because the dot product must = 0....
:-/

2. There is more than one answer to this problem.

3. Hello, stones44!

Find an equation of a plane that is perpendicular to the plane $x-2y+z\:=\:7$
There is an infinite number of answers . . .
A door is perpendicular to the floor. .Swing the door
. . and you have thousands of planes perpendicular to the floor.

Our plane can go through any point, say, $P(5,\,6,\,7)$

Its normal vector, $\vec{n} \:=\:\langle a,\,b,\,c\rangle$, must be perpendicular to $\langle 1,\,\text{-}2,\,1\rangle$

Hence, we have: . $a - 2b + c \:=\:0$

. . We can use, for example: . $\vec{n} \:=\:\langle3,\,2,\,1\rangle$

The equation is: . $3(x-5) + 2(y-6) + 1(z-7)\:=\:0$

. . . . . . . . . . . . $\boxed{3x + 2y + z \:=\:34}$