1. The problem describes a semicircle drawn on a horizontal line segment with its diameter coinciding with the segment. 2. The semicircle is centered on the horizontal line, and an arrow points outward from the curved surface at the top. 3. This setup is often used in vector calculus or physics to represent a unit vector normal to a surface. 4. The unit vector \( \mathbf{k} \) is typically defined as the vector perpendicular (normal) to the plane of the horizontal line, pointing upward. 5. The length of a unit vector is always 1, so \( |\mathbf{k}| = 1 \). 6. The arrow on top of the semicircle indicates the direction of \( \mathbf{k} \), which is perpendicular to the horizontal line segment. 7. In summary, \( \mathbf{k} \) is the unit vector normal to the plane of the horizontal line segment, pointing upward from the semicircle's curved surface. Final answer: \( \mathbf{k} \) is the unit vector normal to the horizontal plane, pointing upward.