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I just started grad school from an engineering background. My research has led me to need more physics & math which is why I'm in the class, but I don't have a very broad Math background. This problem given is exactly as it is typed above. The text we are using is Arfken: Math Methods for Physicists (7th).

Separate [itex]\vec{v}[/itex] into [itex]\vec{g_{1}}[/itex] and [itex]\vec{g_{2}}[/itex].

(It has a figure with the 3 vectors listed above all starting from the same point. No angles or magnitudes are given.

I know that I am suppose to use the curl to find [itex]\vec{v^{1}}[/itex] and somehow there is abstract algebra involved as I've asked for help and that is what he told me. The weird thing is that I don't see how I work what the hint says in with the curl advice. I can do the arithmetic involved (ie I can take vector & scalar products, etc), but I'm just not even sure where to start to end up with the "Result". This is due tonight (I'm not asking for the answer here, just to be clear) so I will update the post as/if I figure more out. At this point I am just looking for advice in general as I am clueless as to what the "path" is if that makes sense.

## Homework Statement

Separate [itex]\vec{v}[/itex] into [itex]\vec{g_{1}}[/itex] and [itex]\vec{g_{2}}[/itex].

(It has a figure with the 3 vectors listed above all starting from the same point. No angles or magnitudes are given.

## Homework Equations

__Hint__:use [itex]\vec{v}[/itex]=[itex]\vec{v^{i}}[/itex][itex]\vec{g_{i}}[/itex], apply from the right the vector product with [itex]\vec{g_{2}}[/itex] and use the dot product to obtain [itex]\vec{g^{1}}[/itex]; [itex]\vec{g^{2}}[/itex] analogous__Result__: [itex]\vec{v}=\vec{g_{2}}\frac{(\vec{g_{1}} x\vec{g_{2}})\ldot(\vec{g_{1}} x \vec{v})}{(\vec{g_{1}} x \vec{g_{2}})^{2}}-\vec{g_{1}}\frac{(\vec{g_{1}} x\vec{g_{2}})\ldot(\vec{g_{2}} x \vec{v})}{(\vec{g_{1}} x \vec{g_{2}})^{2}}[/itex]## The Attempt at a Solution

I know that I am suppose to use the curl to find [itex]\vec{v^{1}}[/itex] and somehow there is abstract algebra involved as I've asked for help and that is what he told me. The weird thing is that I don't see how I work what the hint says in with the curl advice. I can do the arithmetic involved (ie I can take vector & scalar products, etc), but I'm just not even sure where to start to end up with the "Result". This is due tonight (I'm not asking for the answer here, just to be clear) so I will update the post as/if I figure more out. At this point I am just looking for advice in general as I am clueless as to what the "path" is if that makes sense.

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