Final answer:
The student's question requires an understanding of vector operations, including antiparallel vectors, cross products, and calculating the magnitude and direction of vectors in coordinate systems.
Step-by-step explanation:
The student's question involves finding the results of various operations with vectors in a coordinate system. The subject matter includes learning how a vector can be antiparallel to another by multiplying it by a negative scalar, understanding the cross product of unit vectors, and using these principles to solve problems related to vector magnitudes and directions.
Examples in the question demonstrate the algebra of vectors, cross product rules using cyclic order, and determining magnitudes and directions of vectors from their components.