Re: Proving planes are not parallel

From: Virgil (ITSnetNOTcom#virgil_at_COMCAST.com)
Date: 12/05/04 

Date: Sun, 05 Dec 2004 14:51:45 -0700

In article <MvAsd.59737$K7.57296@news-server.bigpond.net.au>,
 Cassandra Thompson <newsgroups@calebsoftware.com> wrote:

> The definition that I have is as follows:
> Two planes are parallel if their normal vectors are parallel, that is,
> if the cross product of their normal vectors is zero.
>
> However my understanding is that a cross product yields another vector,
> not a scalar. So I am confused.

There is a zero vector in every vector space, such that if 0 is the zero
scalar and Z is the zero vector and "." indicates product of scalar with
vector then 0.Z = Z

Since it is usually obvious from the context when a zero object is to be
a scalar and when a vector, the same word is used ambiguously for both,
as in this case.

To say that the cross product of two vectors is zero clearly must mean
the zero vector, not the zero scalar.

Does this clear things up a bit?

>...

> Thanks,
> Cassandra

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