Introduction to Scalar and Vector Analysis

Fundamental vocabulary covering scalars, vectors, and their properties as described in the introductory material for vector analysis and physics.

Scalar

Physical quantities which can be completely described by their magnitude, specified by a number and a unit.

Vector

Physical quantities which need magnitude as well as direction for their complete description, such as displacement, velocity, and force.

Magnitude

The numerical size of a physical quantity, represented by a number and a unit (e.g., in a length of $2\,\text{m}$, the number $2$ is the magnitude).

Tail

The starting point of a directed line segment or arrow that represents a vector.

Head

The end point or arrow head of a directed line segment that represents a vector.

Zero vector (Null vector)

A vector having zero magnitude with an arbitrary direction, symbolically represented as $\vec{0}$.

Displacement

A vector quantity representing the final position of an object relative to its initial position, described by magnitude and direction.

Distance

A scalar quantity representing the total path length traveled, which does not define the final position relative to the start.

Velocity vector of a stationary particle

A specific example of a zero vector.

Vector representation symbol

Vectors are represented by a single capital letter with an arrow above it, such as $\vec{X}$ or $\vec{A}$, or by the symbol $\vec{PQ}$ for a segment from point P to Q.

Vector Magnitude Symbol

The magnitude of a vector $\vec{X}$ is symbolically written as $|\vec{X}|$.