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February 4th, 2015, 04:55 AM  #1 
Newbie Joined: May 2014 From: Singapore Posts: 11 Thanks: 0  Scalar triple product and abstract vector space
Dear all, Can anyone please explain how the linear combination of noncoplanar and nonorthogonal 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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abstract, product, scalar, space, triple, vector 
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