I have been searching for a way to relate known concepts (known to me) to the computation of the dot product in an effort to understand why it takes the form it does. I ran into a little snippet in a classical dynamics book that seems like it just may be the ticket.(adsbygoogle = window.adsbygoogle || []).push({});

Here is what it says:

From analytical geometry we recall that the formula for the cosine of the angle between two line segments is

[tex]cos (\theta) = \frac{A_{x}B_{x}+A_{y}B_{y}+A_{z}B_{z}}{(A_{x}^{2}+A_{y}^{2}+A_{z}^{2})^{1/2}(B_{x}^{2}+B_{y}^{2}+B_{z}^{2})^{1/2}}[/tex]

Then by rearranging and using a definition of dot product we get:

[tex]\vec{A}\bullet\vec{B} := A_{x}B_{x}+A_{y}B_{y}+A_{z}B_{z}[/tex]

[tex]\vec{A}\bullet\vec{B} = cos(\theta)(A_{x}^{2}+A_{y}^{2}+A_{z}^{2})^{1/2}(B_{x}^{2}+B_{y}^{2}+B_{z}^{2})^{1/2}[/tex]

So the real question is: where in analytical geometry can I find this formula for the cosine of the angle between two line segments?

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# Dot, Scalar, Inner Product Question

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