# How to find out of planes are perpendicular

• April 22nd 2009, 11:51 AM
supersaiyan
How to find out if planes are perpendicular
Determine if planes in each pair are parallel, perpendicular, or neither.
$\pi_{1}: 4x-5y+z-9=0$
$\pi_{2}: 2x-9y+z-2=0$
This is what I did
n1 :[4, -5, 1]
n2:[2, -9, 1]

Dot product of n1 and n2 is not zero, so it's neither?

$\pi_{1}: 5x-6y+2z-2=0$
$\pi_{2}: 2x-5y+-20z-2=0$
This is what I did
n1 :[5, -6, 2]
n2:[2, -5, -20]

Dot product of n1 and n2 is zero

What does that mean, is it parallel or perpendicular?

and how do you find out if it's parallel or perpendicular

Thanks
• April 22nd 2009, 12:34 PM
TheEmptySet
Quote:

Originally Posted by supersaiyan
Determine if planes in each pair are parallel, perpendicular, or neither.
$\pi_{1}: 4x-5y+z-9=0$
$\pi_{2}: 2x-9y+z-2=0$
This is what I did
n1 :[4, -5, 1]
n2:[2, -9, 1]

Dot product of n1 and n2 is not zero, so it's neither?

$\pi_{1}: 5x-6y+2z-2=0$
$\pi_{2}: 2x-5y+-20z-2=0$
This is what I did
n1 :[5, -6, 2]
n2:[2, -5, -20]

Dot product of n1 and n2 is zero

What does that mean, is it parallel or perpendicular?

and how do you find out if it's parallel or perpendicular

Thanks

Two planes are parallel if their normal vectors are parallel.

i.e one is a multiple of the other

Two planes are perpendicular if their normal vectors are perpendicular.

remember two vectors are perpendicular if their dot product is 0.

If neither of the above to hold they are neither.

I hope this helps