\begin{definition}[Definition:Right-Hand Rule/Cross Product]
Let $\mathbf a$ and $\mathbf b$ be vector quantities.
The '''right-hand rule''' for the vector cross product $\mathbf a \times \mathbf b$ is a consequence of the determinant definition:
:$\mathbf a \times \mathbf b = \begin{vmatrix}
\mathbf i & \mathbf j & \mathbf k\\
a_i & a_j & a_k \\
b_i & b_j & b_k \\
\end{vmatrix}$
when embedded in the conventional right-hand Cartesian $3$-space:
:450px
Let a '''right hand''' be placed such that:
:the thumb and index finger are at right-angles to each other
:the $3$rd finger is at right-angles to the thumb and index finger, upwards from the palm
:the thumb points along the direction of $\mathbf a$
:the index finger points along the direction of $\mathbf b$.
Then the $3$rd finger is pointed along the direction of $\mathbf a \times \mathbf b$.
:400px
\end{definition}