Final answer:
The expression F(x, y, z) represents a vector field because it assigns a vector to every point in three-dimensional space, with components dependent on the coordinates x, y, and z.
Step-by-step explanation:
The expression F(x, y, z) = yz sin(xy) i + xz sin(xy) j - cos(xy) k represents a vector field. This is because the function F assigns a vector to every point in three-dimensional space, with the individual components of this vector varying based on their respective coordinates x, y, and z.
By analyzing the components of F, we observe that they include products and trigonometric functions of the coordinates, indicating a spatial dependence that suggests a vector field. Unlike scalar fields, which associate a single value to each point in space, vector fields describe a distribution of vectors, which is evident in the given function with its i, j, and k components.
Furthermore, this vector field does not represent the curl or divergence of another vector field, as it is not expressed as the result of applying differential operators on another given vector field.