Final answer:
The rotation is not about the primary x, y, or z axes but about a diagonal axis defined by the vector (0, 1, 1); therefore, none of the options a, b, or c are correct, and the answer is d) No rotation.
Step-by-step explanation:
The student is asking about the representation of a rotation by 45 degrees about an axis defined by a vector. The given vector is (0, 1, 1), which indicates that the rotation axis is a line that passes through the origin and has direction components along the y-axis and z-axis. Therefore, it is not a rotation about the x-axis, y-axis, or z-axis exclusively; it is a rotation about an axis that is a combination of the y-axis and z-axis. Thus, none of the standard axes (x, y, z) are the correct answer, so it is not (a), (b), or (c). Hence, the answer would be (d) No rotation, because the question may imply that it is looking for a rotation about one of the primary axes exclusively, which is not the case here.