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@ -254,11 +254,12 @@ $`=dx\;\overrightarrow{e_x}+dy\;\overrightarrow{e_y}+dz\;\overrightarrow{e_z}`$< |
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[EN] y its norm (or length) is thescalar line element :<br> |
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[EN] y its norm (or length) is thescalar line element :<br> |
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<br>$`||\overrightarrow{dl}||=\sqrt{dl_x^2+dl_y^2+dl_z^2}=\sqrt{dx^2+dy^2+dz^2}`$<br> |
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<br>$`||\overrightarrow{dl}||=\sqrt{dl_x^2+dl_y^2+dl_z^2}=\sqrt{dx^2+dy^2+dz^2}`$<br> |
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<br>$`||\overrightarrow{dl}||=\sqrt{\overrightarrow{dl}\cdot\overrightarrow{dl}}`$ |
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<br>$`||\overrightarrow{dl}||=\sqrt{\overrightarrow{dl}\cdot\overrightarrow{dl}}`$ |
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$`=\sqrt{(dl_x\;\overrightarrow{e_x}+dl_y\;\overrightarrow{e_y}+dl_z\;\overrightarrow{e_z})\cdot |
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(dl_x\;\overrightarrow{e_x}+dl_y\;\overrightarrow{e_y}+dl_z\;\overrightarrow{e_z})}`$ |
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$`=\left[(dl_x\;\overrightarrow{e_x}+dl_y\;\overrightarrow{e_y}+dl_z\;\overrightarrow{e_z})\cdot |
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(dl_x\;\overrightarrow{e_x}\rigth.`$ |
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$`\left.+dl_y\;\overrightarrow{e_y}+dl_z\;\overrightarrow{e_z})\right]^{1/2}`$ |
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$`=\left[(dl_x)^2\;(\overrightarrow{e_x}\cdot\overrightarrow{e_x})\right.`$ |
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$`=\left[(dl_x)^2\;(\overrightarrow{e_x}\cdot\overrightarrow{e_x})\right.`$ |
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$`+(dl_y)^2\;(\overrightarrow{e_y}\cdot\overrightarrow{e_y})`$ |
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$`+(dl_y)^2\;(\overrightarrow{e_y}\cdot\overrightarrow{e_y})`$ |
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$`+(dl_z)^2\;(\overrightarrow{e_z}\cdot\overrightarrow{e_z})}`$ |
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$`+(dl_z)^2\;(\overrightarrow{e_z}\cdot\overrightarrow{e_z})`$ |
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$`+(2\,dl_x\,dl_y)\,(\overrightarrow{e_x}\cdot\overrightarrow{e_y})`$ |
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$`+(2\,dl_x\,dl_y)\,(\overrightarrow{e_x}\cdot\overrightarrow{e_y})`$ |
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$`+(2\,dl_x\,dl_z)\,(\overrightarrow{e_x}\cdot\overrightarrow{e_z})`$ |
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$`+(2\,dl_x\,dl_z)\,(\overrightarrow{e_x}\cdot\overrightarrow{e_z})`$ |
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$`\left.+(2\,dl_y\,dl_z)\,(\overrightarrow{e_y}\cdot\overrightarrow{e_z})\right]^{1/2}`$ |
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$`\left.+(2\,dl_y\,dl_z)\,(\overrightarrow{e_y}\cdot\overrightarrow{e_z})\right]^{1/2}`$ |
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