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# Direction Cosines

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1. Bit confused here:

It says a_ij is the i component in the E system of ej (e with a line on top).

Does this mean to say that the unit vector in the second co-ordinate system, ej (with a line on top), has components which can be mapped on the first system, which is precisely what a_ij is?
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2. (Original post by djpailo)
Bit confused here:

It says a_ij is the i component in the E system of ej (e with a line on top).

Does this mean to say that the unit vector in the second co-ordinate system, ej (with a line on top), has components which can be mapped on the first system, which is precisely what a_ij is?
Yes.

Any vector can be split into compoments.

E and bar{E} (sorry, LaTex is still shot), are two different coordinate systems mapping the same space. Any vector can be described in terms of either coordinate system.

In partiuclar, bar{ej} can be written as a sum of the ei's and is actually sum (i=1 to n) aij ei

The coefficient aij relates to the projection of bar{ej} onto ei, and because they are both unit vectors, this works out to be the cosine of the angle between bar{ej} and ei, that is it's a direction cosine.

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