Final Answer:
||u * v|| = || u || * || v|| u and v are orthogonal u and v are perpendicular (option b).
Step-by-step explanation:
The equation ||u * v|| = ||u|| * ||v|| holds true when u and v are orthogonal, indicating that they are perpendicular vectors. This mathematical relationship arises from the definition of the dot product of orthogonal vectors. In the context of this question, the dot product u * v results in a scalar value, and the magnitude of this scalar product is equal to the product of the magnitudes of u and v when the vectors are orthogonal (option b).
Mathematically, this relationship is expressed as ||u * v|| = ||u|| * ||v||. If u and v are orthogonal, their dot product u * v equals 0, and the equation simplifies to ||0|| = ||u|| * ||v||, which is a true statement. This condition of orthogonality implies that the vectors u and v form a right angle with each other.
In summary, option B) u and v are perpendicular is the correct choice. It accurately reflects the mathematical condition expressed in the given equation, providing a concise and accurate response to the question about the relationship between vectors u and v when the magnitudes of their cross product and individual magnitudes are considered.