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How do I prove that dot product of two free vectors ( inner product in 2D and 3D vectors) does not depend on the choice of frames in which their coordinates are defined?

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    1) What do you mean by a "frame" ? 2) What do you mean by a "dot" product?2011-02-03
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    frame = basis (it's a more physical terminology) and dot product is scalar product.2011-02-03
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    You should state what definition of dot product you are using.2011-02-03
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    3) What do you mean by a 'free vector'?2011-02-03
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    probably linearly independent, and frame probably means orthonormal basis.2011-02-03
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    Because the dot product is defined in a coordinate-independent fashion: $\mathbf x \cdot \mathbf y = |\mathbf x| |\mathbf y|\cos\left(\angle\mathbf x\mathbf y\right)$.2011-02-03

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