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January 21, 2017
Posted by **kelsey** on Thursday, May 10, 2012 at 5:14pm.

- Analytic Geometry -
**MathMate**, Friday, May 11, 2012 at 6:06pmGiven two planes:

Π1 : Ax+By+Cz+D=0 and

Π2 : ax+by+cz+d=0

The following uses the notation that

<a,b,c> represents a vector with three components.

The normal vectors are:

N1 : <A,B,C>

N2 : <a,b,c>

If Π1 is perpendicular to Π2, then

N1.N2=0 (dot-product).

If the planes are parallel, we can find a numeric factor α such that

<A,B,C>=α<a,b,c>

If in addition, D=αd, then the planes are coincident.

If no such α can be found, the planes are not parallel.