More Planes

**stones44** · January 12th 2008, 12:01 PM

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....
:-/

**ThePerfectHacker** · January 12th 2008, 02:27 PM

There is more than one answer to this problem.

**Soroban** · January 12th 2008, 02:33 PM

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

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

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