Sunday

April 20, 2014

April 20, 2014

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.

**Related Questions**

Laboratory (math, chemistry) - Most analytic methods are subject to drift. ...

Math - intersection of planes - You are given the following two planes: x+4y-3z-...

Math - intersection of planes - You are given the following two planes: x+4y-3z-...

Calculus - Consider the planes given by the equations 2y−2x−z=2 x&#...

Linear Algebra 2 - This is another question I can't figure out. Given planes ...

analytical geometry - show that the locus of a point whose distances from two ...

analytical geometry - show that the locus of a point whose distances from two ...

psychology - Can I please have some information to help me discuss this question...

Geometry Honors (p.2) - Two planes that lie in parallel planes are ________. ...

history - The Spanish, French, and English all explored America and left a ...