Final answer:
The cross products uv and vu can be found using the components of the vectors u and v, with the cross product being anticommutative, meaning uv = -vu. The direction of the cross product will be perpendicular to both u and v.
Step-by-step explanation:
When we want to find the cross products uv and vu for the vectors u and v, we can utilize the cross-product formula C = A × B where C is the resultant vector and A and B are the original vectors. The resultant vector components are given by Cx = Ay Bz - Az By, Cy = Az Bx - Ax Bz, and Cz = Ax By - Ay Bx. This operation is particularly important in physics and engineering as it yields a vector perpendicular to the original vectors, which is useful for finding the direction of factors such as torque, force, and angular momentum. The cross product is also anticommutative, which means that uv is not the same as vu; instead, they are opposite in direction: uv = -vu. To compute uv and vu, you would use the components of u and v, apply the formula accordingly and remember to switch the signs for the resultant vectors of vu to show they are opposites.