Final answer:
This question pertains to vector multiplication and cross products in vector algebra, an area of high school level Mathematics. It requires knowledge of unit vectors, trigonometric identities, and vector properties to solve for vector magnitudes and directions. The expressions involve the Cartesian unit vectors i, j, and k.
Step-by-step explanation:
The question involves vector multiplication and calculating the cross product of vectors, which falls under the subject of Mathematics, specifically in the area of vector algebra. The notation u, i, j, and k typically represents vectors and unit vectors in the Cartesian coordinate system.
The question likely originates from a high school physics or mathematics curriculum that includes topics on forces, electromagnetism, or vector analysis.
To solve the problem provided in the question, one would need to follow the rules of vector operations, such as cross products and dot products. Understanding these concepts is essential for solving physics problems involving forces, motion, and fields. The expressions involving unit vectors i, j, and k refer to the unit vectors in the x, y, and z directions, respectively.
Magnitude and direction are fundamental aspects when working with vectors. The provided equations demonstrate the use of trigonometric identities and vector properties to find vector magnitudes and directions. These processes require a solid understanding of vector algebra and trigonometry, likely at the high school level.