Study guide and 1 practice problem on:

Cross products of i, j, and k

$\newcommand{\bfA}{\mathbf{A}}$ $\newcommand{\bfB}{\mathbf{B}}$ $\newcommand{\bfC}{\mathbf{C}}$ $\newcommand{\bfF}{\mathbf{F}}$ $\newcommand{\bfI}{\mathbf{I}}$ $\newcommand{\bfa}{\mathbf{a}}$ $\newcommand{\bfb}{\mathbf{b}}$ $\newcommand{\bfc}{\mathbf{c}}$ $\newcommand{\bfd}{\mathbf{d}}$ $\newcommand{\bfe}{\mathbf{e}}$ $\newcommand{\bfi}{\mathbf{i}}$ $\newcommand{\bfj}{\mathbf{j}}$ $\newcommand{\bfk}{\mathbf{k}}$ $\newcommand{\bfn}{\mathbf{n}}$ $\newcommand{\bfr}{\mathbf{r}}$ $\newcommand{\bfu}{\mathbf{u}}$ $\newcommand{\bfv}{\mathbf{v}}$ $\newcommand{\bfw}{\mathbf{w}}$ $\newcommand{\bfx}{\mathbf{x}}$ $\newcommand{\bfy}{\mathbf{y}}$ $\newcommand{\bfz}{\mathbf{z}}$
$\bfi \times \bfj = \bfk$, $\quad \bfj \times \bfk = \bfi$, $\quad \bfk \times \bfi = \bfj$.

$\bfj \times \bfi = -\bfk$, $\quad \bfk \times \bfj = -\bfi$, $\quad \bfi \times \bfk = -\bfj$.
Note that the coefficient of the cross product is positive if the order of the vectors is given by $\bfi \to \bfj \to \bfk \to \bfi$. It is negative if the order of the vectors is in the opposite order.

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