Math Is Fun Forum

NoSash

Member

Registered: 2006-02-06

Posts: 7

Vector Cross and Dot Product

See the image, show using the diagram...
I have no idea how to apply the diagram.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: Vector Cross and Dot Product

This is called the scalar triple product. It is given by [a, b, c] where a, b, and c are the three vectors. You can understand this better if you know determinants. This can be of some help. And this one too.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Vector Cross and Dot Product

There are two ways to explain this.  Either geometrically or algebraically.

To do it algebraically, just do:

a = <a1, a2, a3>
b = <b1, b2, b3>
c = <c1, c2, c3>

And then compute each dot/cross product.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

NoSash

Member

Registered: 2006-02-06

Posts: 7

Re: Vector Cross and Dot Product

Yes I know how to prove it algebraically... just not with the diagram.
I'm going to check out your links, thanks ganesh.

Last edited by NoSash (2006-03-18 05:00:19)

NoSash

Member

Registered: 2006-02-06

Posts: 7

Re: Vector Cross and Dot Product

eh... if anyone is interested in the solution, here it is:

It's really simple actually... Because it is a CIRCLE, 2-dimensional shape, the scalar triple products are all equal to zero...
Three vectors in a 2D plane are always linearly dependent.

fgarb

Member

Registered: 2006-03-03

Posts: 89

Re: Vector Cross and Dot Product

That's a very strange diagram. The equalities you wrote down are definitely true for the case where all three vectors are in the same plane as you said, but just to make sure you understand, these forumulas are also true for any three vectors.