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Format improvement on equation
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content/ai/math/algebra/vectors/index.en.md

Lines changed: 5 additions & 9 deletions
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@@ -218,15 +218,11 @@ $$
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Expanding the left side:
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$$
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\|\mathbf{u} - \mathbf{v}\|^2 = \|\mathbf{u}\|^2 + \|\mathbf{v}\|^2 - 2 \|\mathbf{u}\| \|\mathbf{v}\| \cos(\theta)
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$$
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$$
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(\mathbf{u} - \mathbf{v}) \cdot (\mathbf{u} - \mathbf{v}) = \|\mathbf{u}\|^2 + \|\mathbf{v}\|^2 - 2 \|\mathbf{u}\| \|\mathbf{v}\| \cos(\theta)
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$$
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$$
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\|\mathbf{u}\|^2 - 2 (\mathbf{u} \cdot \mathbf{v}) + \|\mathbf{v}\|^2 = \|\mathbf{u}\|^2 + \|\mathbf{v}\|^2 - 2 \|\mathbf{u}\| \|\mathbf{v}\| \cos(\theta)
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\begin{aligned}
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\|\mathbf{u} - \mathbf{v}\|^2 = \|\mathbf{u}\|^2 + \|\mathbf{v}\|^2 - 2 \|\mathbf{u}\| \|\mathbf{v}\| \cos(\theta) \\
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(\mathbf{u} - \mathbf{v}) \cdot (\mathbf{u} - \mathbf{v}) = \|\mathbf{u}\|^2 + \|\mathbf{v}\|^2 - 2 \|\mathbf{u}\| \|\mathbf{v}\| \cos(\theta) \\
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\|\mathbf{u}\|^2 - 2 (\mathbf{u} \cdot \mathbf{v}) + \|\mathbf{v}\|^2 = \|\mathbf{u}\|^2 + \|\mathbf{v}\|^2 - 2 \|\mathbf{u}\| \|\mathbf{v}\| \cos(\theta)
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\end{aligned}
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$$
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Cancelling \(\|\mathbf{u}\|^2\) and \(\|\mathbf{v}\|^2\) from both sides:

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