- #1

- 106

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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 is

##

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 non-coplanar and non-orthogonal 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...