Formula:157

Digital Library of Mathematical Functions ID 1.6.E9

${\displaystyle{\displaystyle\mathbf{a}\times\mathbf{b}=\begin{vmatrix}\mathbf{i}&\mathbf{j}&\mathbf{k}\\ a_{1}&a_{2}&a_{3}\\ b_{1}&b_{2}&b_{3}\end{vmatrix}\\ =(a_{2}b_{3}-a_{3}b_{2})\mathbf{i}+(a_{3}b_{1}-a_{1}b_{3})\mathbf{j}+(a_{1}b_{2}-a_{2}b_{1})\mathbf{k}\\ =\|\mathbf{a}\|\|\mathbf{b}\|(\sin\theta)\mathbf{n},}}$

Symbols List

• ${\displaystyle{\displaystyle\det}}$:
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle\theta}}$: angle between a and b
• ${\displaystyle{\displaystyle\mathbf{i}}}$: unit vector
• ${\displaystyle{\displaystyle\mathbf{j}}}$: unit vector
• ${\displaystyle{\displaystyle\mathbf{k}}}$: unit vector
 

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