 #1
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Dear all,
Can anyone please explain how the linear combination of noncoplanar and nonorthogonal coordinate axes representing a point x as shown below 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.
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x = \dfrac{[x,b,c]}{[a,b,c]} a + \dfrac{[a,x,c]}{[a,b,c]} b + \dfrac{[a,b,x]}{[a,b,c]} c
##
I know that you can just add up the 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
## \dfrac{[x,b,c]}{[a,b,c]} , \dfrac{[a,x,c]}{[a,b,c]} and \dfrac{[a,b,x]}{[a,b,c]} ##
Danke...
Can anyone please explain how the linear combination of noncoplanar and nonorthogonal coordinate axes representing a point x as shown below 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.
##
x = \dfrac{[x,b,c]}{[a,b,c]} a + \dfrac{[a,x,c]}{[a,b,c]} b + \dfrac{[a,b,x]}{[a,b,c]} c
##
I know that you can just add up the 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
## \dfrac{[x,b,c]}{[a,b,c]} , \dfrac{[a,x,c]}{[a,b,c]} and \dfrac{[a,b,x]}{[a,b,c]} ##
Danke...
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