Wednesday

November 26, 2014

November 26, 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.

**Answer this Question**

**Related Questions**

math - ) Determine whether the following two planes x + 4y − z = 7 and 5x...

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&#...

Calculus - Determine if the planes in each pair are parallel and distinct or ...

Math: Scalar Equations of a Plane - Find the scalar equation of each of the ...

Geometry - Planes A and B are both perpendicular to line M. What is the ...

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

Math: Scalar Equation of a Plane - Determine whether the following pairs of ...

multivariable calculus - Consider the surface given by the equation: 2x2 - 3z2...