Final answer:
The student's question is about defining the set W that consists of all vectors on a unit circle in R², connecting to concepts in linear algebra and vector calculus.
Step-by-step explanation:
The student's question pertains to a set W which is defined within the mathematical field of linear algebra, a subset of R² (the two-dimensional real number plane). The set W comprises all vectors in R² such that the sum of the squares of their components equals 1. This equation represents a circle with a radius of 1 centered at the origin in the Cartesian coordinate system.
The magnitude of a vector is the square root of the sum of the squares of its components, and this is derived from the Pythagorean theorem. When considering vectors in R², the direction of the vector can be defined by the direction angle, which is measured counterclockwise from the positive x-axis. The x and y components of a vector can be expressed as the product of the vector's magnitude and the cosine and sine of its direction angle, respectively.