Final answer:
The length of the directed line segment PQ is denoted by ||PQ||, representing the magnitude or distance between the points P and Q. Magnitude is a scalar expressing the size of the vector, calculated using the Pythagorean theorem.
Step-by-step explanation:
The length of the directed line segment PQ is denoted by ||PQ||. This notation ||PQ|| represents the magnitude or the distance between points P and Q in whichever space they are defined, whether it be on a plane for two-dimensional vectors or in three-dimensional space.
In the context of vectors, magnitude is a term that describes the length or the size of the vector. The magnitude is always a positive scalar quantity, and when considering a vector in two or three dimensions, it can be calculated using the Pythagorean theorem based on the vector's components.
For example, in two dimensions, if vector PQ has components (x, y), then the magnitude (||PQ||) can be calculated using the equation ||PQ|| = √x² + y². In three dimensions, if the vector has components (x, y, z), the formula extends to ||PQ|| = √x² + y² + z².