My Math Forum Scalar triple product and abstract vector space

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February 4th, 2015, 04:55 AM   #1
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Scalar triple product and abstract vector space

Dear all,
Can anyone please explain how the linear combination of non-coplanar and non-orthogonal coordinate axes representing a point x as shown below in the attachment is derived. Please use the reference text attached in this post to explain to me as i will find it a bit relevant. I want to know how it is derived using the scalar triple product and to get an understanding of what a scalar triple product does to three vectors apart from it calculating the volume of the parrellelepiped formed from the three vectors.

I know that you can just add up the magnitudes in the directions of the axes a,b and c to locate a point x. but how did the magnitudes in the direction a,b and c come to be

[x,b,c]/[a,b,c],[a,x,c]/[a,b,c]and[a,b,x]/[a,b,c]

Danke...
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 Tags abstract, product, scalar, space, triple, vector

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