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@ -256,11 +256,12 @@ $`=dx\;\overrightarrow{e_x}+dy\;\overrightarrow{e_y}+dz\;\overrightarrow{e_z}`$< |
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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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$`=\sqrt{(dl_x\;\overrightarrow{e_x}+dl_y\;\overrightarrow{e_y}+dl_z\;\overrightarrow{e_z})\cdot |
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$`=\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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(dl_x\;\overrightarrow{e_x}+dl_y\;\overrightarrow{e_y}+dl_z\;\overrightarrow{e_z})}`$ |
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$`=\sqrt{dl_x^2\;(\overrightarrow{e_x}\cdot\overrightarrow{e_x})+dl_y^2\;(\overrightarrow{e_y}\cdot\overrightarrow{e_y}) +dl_z^2\;(\overrightarrow{e_z}\cdot\overrightarrow{e_z})`$ |
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$`+2\,dl_x\,dl_y\,x(\overrightarrow{e_x}\cdot\overrightarrow{e_y})`$ |
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$`+2\,dl_x\,dl_z\,x(\overrightarrow{e_x}\cdot\overrightarrow{e_z})`$ |
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$`+2\,dl_y\,dl_z\,x(\overrightarrow{e_y}\cdot\overrightarrow{e_z})}`$ |
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$`=\sqrt{dl_x^2+dl_y^2+dl_z^2}`$ |
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$`=\sqrt{(dl_x)^2\;(\overrightarrow{e_x}\cdot\overrightarrow{e_x})+(dl_y)^2\;(\overrightarrow{e_y}\cdot\overrightarrow{e_y}) |
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+(dl_z)^2\;(\overrightarrow{e_z}\cdot\overrightarrow{e_z})`$ |
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$`+(2\,dl_x\,dl_y)\,(\overrightarrow{e_x}\cdot\overrightarrow{e_y})`$ |
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$`+(2\,dl_x\,dl_z)\,(\overrightarrow{e_x}\cdot\overrightarrow{e_z})`$ |
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$`+(2\,dl_y\,dl_z)\,(\overrightarrow{e_y}\cdot\overrightarrow{e_z})}`$ |
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$`=\sqrt{(dl_x)^2+(dl_y)^2+(dl_z)^2}`$ |
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$`=\sqrt{dx^2+dy^2+dz^2}`$ |
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$`=\sqrt{dx^2+dy^2+dz^2}`$ |
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