Cross Product (Vector Product)

Definition

$$ \vec{A} \times \vec{B} = AB \sin\theta \ \hat{n} $$

Determinant Form

$$ \vec{A} \times \vec{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ A_x & A_y & A_z \\ B_x & B_y & B_z \end{vmatrix} $$

Physical Meaning

The cross product gives a vector perpendicular to both vectors.

Example: Torque

$$ \vec{\tau} = \vec{r} \times \vec{F} $$