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| 183_notes:cross_product [2014/11/18 15:31] – caballero | 183_notes:cross_product [2014/11/18 15:33] (current) – caballero | ||
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| We further cross-multiply to find the determinants of the 2-by-2 matrices, | We further cross-multiply to find the determinants of the 2-by-2 matrices, | ||
| - | $$\vec{B} \times \vec{C} = \hat{x}\left(B_yC_z - C_yB_z\right)- \hat{y} \left(B_x C_z - C_xB_z\right) + \hat{z} (B_xC_y - C_xB_y\right)$$ | + | $$\vec{B} \times \vec{C} = \hat{x}\left(B_yC_z - C_yB_z\right)- \hat{y} \left(B_x C_z - C_xB_z\right) + \hat{z} |
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| + | So, in general, the cross product in Cartesian coordinates is given by, | ||
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| + | $$\vec{B} \times \vec{C} = \langle B_yC_z - C_yB_z, C_xB_z-B_x C_z, B_xC_y - C_xB_y\rangle$$ | ||