Question

Points P and Q are at the following locations on a number line. P is at 5. Q is at -1. Which number is on vec (PQ) but not on vec (QP) ?

Answer 1

Vectors typically describe both magnitude and direction, so there would not be a number on vector PQ that is not also on vector QP, as they merely represent direction and distance between the same two points in opposite order.

Step-by-step explanation:

The student has asked about vectors on a number line. Vector PQ represents a displacement from point P at 5 to point Q at -1, while vector QP represents the opposite, a displacement from point Q at -1 to point P at 5. Since both vectors have the same magnitude but opposite directions, the number on vector PQ that is not on vector QP does not relate to common vector operations as these would typically have the same set of numbers. However, if this question is interpreted in the context of directed line segments, it could be said that the direction from P to Q is associated with vector PQ but not with vector QP. In typical vector operations, there is no number uniquely on one vector and not the other because vectors describe both magnitude and direction.