Hi pf,(adsbygoogle = window.adsbygoogle || []).push({});

Having some trouble with basis vectors for expanding a given vector in 3-D space.

Any given vector in 3-D space can be given by a sum of component vectors in the form:

V = e1V1 + e2V2 + e3V3 (where e1, e2 and e3 are the same as i, j and k unit vectors). Equation 1.

I am happy with this.

If you want to find the coefficient V2 you can do the following:

e2 . V = (ei . e2) Vi = (di2) Vi (the dot in between is supposed to be the dot product and d is supposed to be kronecker's delta). Equation 2.

When i is two then delta i2 is one which means 1 x V2 which equals V2.

Equation 2 is what I am not happy with. I get the equation and I understand what kronecker's delta is but how would this ever help you find the coefficient V2? Let's say that you have some vector of magnitude 5 in a 2-D space then we know the components are 3 (y component) and 4 (x component). Let's say you didn't know the y-component was 3 then how would equation 2 be of any use to you? Equation 2 seems nonsense to me. It just looks like its saying (e2 x e2) V2 = (1) x V2 = V2 which is obvious but I don't see how you can use it to get V2 when you don't know what V2 is which is what my book seems to be implying. Could somebody give me an example of how you would use equation 2 to find a coefficient of a vector?

Thanks in advance for any help offered.

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# Vector Analysis using Basis Vectors

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