向量外積的性質

屬性

$\left( \overrightarrow{a}\times \overrightarrow{b} \right)\bot \overrightarrow{a}$ ， $\left( \overrightarrow{a}\times \overrightarrow{b} \right)\bot \overrightarrow{b}$
$\left| \overrightarrow{a}\times \overrightarrow{b} \right|=\left| \overrightarrow{a} \right|\left| \overrightarrow{b} \right|\sin \theta =\overrightarrow{a},\overrightarrow{b}$ 所圍成平行四邊形之面積。註： $\theta \,$ 為 $\overrightarrow{a}$ ， $\overrightarrow{b}$ 之夾角
$\Delta =\frac{1}{2}\times \left| \overrightarrow{a} \right|\times \left| \overrightarrow{b} \right|\times \sin \theta =\frac{1}{2}\left| \overrightarrow{a}\times \overrightarrow{b} \right|$