Cross product

The AP Physics C: Mechanics CED sets it out in three parts under essential knowledge 5.3.B.2. The cross product of two vectors results in a vector quantity of magnitude $AB\sin\theta$. Its direction is perpendicular to both vectors and therefore normal to the plane they define. And that direction is found qualitatively by applying the appropriate right hand rule.

The sine does the opposite job to the dot product's cosine. Perpendicular vectors give the maximum $AB$; parallel or antiparallel vectors give zero. That zero is the physical statement that a force directed straight at the pivot exerts no torque, however hard you push.

Order matters, unlike multiplication of numbers: $\vec{A}\times\vec{B} = -(\vec{B}\times\vec{A})$. Swapping the operands reverses the result, so reversing the two vectors in a torque flips it from counterclockwise to clockwise.

Where it appears: the C: Mechanics sheet prints torque as $\vec{\tau} = \vec{r}\times\vec{F}$ and angular momentum as $\vec{L} = \vec{r}\times\vec{p} = I\vec{\omega}$, and the C: Electricity and Magnetism sheet prints the magnetic force as $\vec{F}_B = q\,\vec{v}\times\vec{B}$.

The vector form belongs to the calculus-based courses. AP Physics 1 and 2 print magnitudes only, $\tau = r_{\perp}F = rF\sin\theta$ and $L = rmv\sin\theta$, and handle direction with a stated sign convention instead.