Calcul vectorial/Produs vectorial

Fie $𝐚 = a_{1} 𝐢 + a_{2} 𝐣 + a_{3} 𝐤, 𝐛 = b_{1} 𝐢 + b_{2} 𝐣 + b_{3} 𝐤$ vectori din $ℝ^{3} .$

Produsul vectorial dintre $𝐚, 𝐛,$ notat $𝐚 \times 𝐛,$ este vectorul:

𝐚 \times 𝐛 = | \begin{matrix} a_{2} & a_{3} \\ b_{2} & b_{3} \end{matrix} | 𝐢 - | \begin{matrix} a_{1} & a_{3} \\ b_{1} & b_{3} \end{matrix} | 𝐣 + | \begin{matrix} a_{1} & a_{2} \\ b_{1} & b_{2} \end{matrix} | 𝐤,

sau simbolic:

𝐚 \times 𝐛 = | \begin{matrix} 𝐢 & 𝐣 & 𝐤 \\ a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \end{matrix} |

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