Final answer:
In geometry, when two points, A and B, lie in the same plane R, then the line AB that joins these points will always lie in the same plane. Some confusion might arise considering vectors, but even vectors A and B form a plane when they are just considered points.
Step-by-step explanation:
The subject of this question falls under Geometry, specifically the behavior of points, lines, and planes. The direct answer in 2 lines is: Points A and B lie in plane R, but line AB can never lie outside of plane R, if both points are part of the plane. This conclusion is based on the fundamentals of plane concept in geometry.
For a step by step explanation, let us consider the definitions. Points, lines, and planes are fundamental concepts in geometry. A plane is a flat, two-dimensional surface that extends indefinitely in all directions. If points A and B are lying on the same plane, then the straight line AB that connects these two points must also lie on the same plane. This behavior adheres to the basic postulates in geometry, particularly Euclid's postulate that states a straight line can be drawn from any point to any other point.
In vector analysis, two vectors can be represented as points, say points A and B for vectors A and B, respectively. These points can be added to produce a resultant vector R. They form an associated plane, in which they are perpendicular to each other. If we look at line AB, it will be within that plane.
Learn more about Geometry