Final answer:
To find the magnitude of u × v, the formula |u| |v| sin(θ) is used, with θ as the angle between the vectors. The direction is determined by the right-hand rule, which indicates whether u × v is into or out of the screen based on the orientation of u and v.
Step-by-step explanation:
The problem involves finding the magnitude of the cross product of two velocity vectors u and v, and determining the direction of this cross product relative to an observer. This is a concept from vector mechanics in physics, specifically dealing with the properties and operations involving vectors.
To find the magnitude |u × v| of the cross product, we use the formula:
Where |u| and |v| are the magnitudes of vectors u and v respectively, and θ is the angle between them. To determine the direction of u × v, we apply the right-hand rule: if you point your index finger in the direction of u, and your middle finger in the direction of v, your thumb will point in the direction of u × v.
If the cross product is directed into the screen, the vectors are arranged such that this right-hand rule orientation would have the thumb pointing away from the observer (into the screen). Conversely, if the cross product is directed out of the screen, the thumb would point towards the observer (out of the screen).