Cross Product

Definition

$\vec{A} \times \vec{B} = | \vec{A} | | \vec{B} | \sin θ \hat{u}$ where $\hat{u} ⊥$ to plane made by $\vec{A}$ & $\vec{B}$ .
$\vec{A} \times \vec{B} = | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ A_{x} & A_{y} & A_{z} \\ B_{x} & B_{y} & B_{z} \end{matrix} | = \hat{i} (A_{y} B_{z} - A_{z} B_{y}) - \hat{j} (A_{x} B_{z} - A_{z} B_{x}) + \hat{k} (A_{x} B_{y} - A_{y} B_{x})$

Triple Cross Product

\vec{A} \times (\vec{B} \times \vec{C}) = \vec{B} (\vec{A} \cdot \vec{C}) - \vec{C} (\vec{A} \cdot \vec{B})