Question

kevin says that lines p and m will eventually intersect. is kevin correct? no, because they are non - coplanar. no, because they are parallel. yes, because they are perpendicular. yes, because they are coplanar.

Explanation:

To determine if Kevin is correct, we analyze the lines \( p \) and \( m \). From the diagram, lines \( p \) and \( m \) lie on the same plane (plane \( A \)), so they are coplanar. Parallel lines (in a plane) never intersect, and perpendicular lines do intersect, but here \( p \) and \( m \) are parallel (indicated by the arrow markings, showing the same direction). Wait, no—wait, the options: the first option says non - coplanar, but \( p \) and \( m \) are on plane \( A \), so they are coplanar. Wait, no, let's re - examine. Wait, the lines \( p \) and \( m \): in the diagram, they are on the same plane (plane \( A \)) and have the same direction (parallel). Parallel lines in a plane never intersect. But wait, the first option says "No, because they are non - coplanar"—but they are on plane \( A \), so that's wrong. The second option: "No, because they are parallel"—parallel lines in a plane don't intersect, so if \( p \) and \( m \) are parallel, they won't intersect. Wait, but let's check the planes. Wait, line \( p \) and line \( m \): looking at the diagram, plane \( A \) is the horizontal plane, and both \( p \) and \( m \) are on plane \( A \). The arrow markings on \( p \) and \( m \) suggest they are parallel (same direction). So parallel lines in a plane do not intersect. So Kevin is incorrect, and the reason is that they are parallel. Wait, but wait, the first option: "non - coplanar"—but they are on the same plane. So the correct option is "No, because they are parallel" (the second option). Wait, no, let's re - check. Wait, the lines \( p \) and \( m \): are they parallel? The arrows on \( p \) and \( m \) are in the same direction, so they are parallel. Parallel lines (in a plane) never intersect. So the answer is the second option: No, because they are parallel.

Answer:

No, because they are parallel. (The option corresponding to this statement in the multiple - choice is the second option: "No, because they are parallel.")