(adsbygoogle = window.adsbygoogle || []).push({}); Different "Versions" of a Plane in R^3 (The Plane!, The Plane!)

Hi, All:

The two most common expressions , AFAIK, for describing a plane in ## R^3 ## are:

i) Writing the plane in the form : ax+by+cz=d

ii) Giving a basis {v_{1}, v_{2}} for the plane.

I know how to produce a basis to go from version i) to version ii) -- basically by using techniques of Gaussian elimination . I know of a method to produce a plane from a pair of basis elements, but I can't see how it works ; we do a cross-product of the basis vectors. I thought this cross-product would just produce a vector normal to the given {v_{1}, v_{2}} , but somehow it generates an equation of the type in i). Does anyone understand why/how this formula works, or know some other nice way to go from version ii), i.e., from a basis, to the form in i)?

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# Different Versions of a Plane in R^3 (The Plane!, The Plane!)

**Physics Forums | Science Articles, Homework Help, Discussion**