Vector (physics)

A physical quantity with magnitude and direction that transforms according to vector rules. Displacement, velocity, and force are examples.

Scalar (physics): A physical quantity specified by magnitude alone, without direction. Scalars such as mass and temperature lack the directional information vectors carry.
Dot product: A scalar-valued operation on two vectors equal to the product of their magnitudes and the cosine of their angle. It extracts the part of one vector aligned with another, as in work.
Displacement: A change in position represented by a directed segment from an initial point to a final point. It is the simplest physical example of a vector quantity.
Pseudovector: A quantity that transforms like a vector under rotations but gains an extra sign under reflections. Angular momentum and torque reveal that direction alone does not determine vector transformation behavior.
Coordinate system: A framework of reference axes or coordinates used to specify positions and directions. Coordinates express a vector's components relative to chosen axes.
Cross product: A three-dimensional vector operation whose direction is perpendicular to its inputs and whose magnitude is their parallelogram area. It produces axial quantities such as torque from pairs of vectors.
Velocity: The rate of change of position with respect to time, including direction. Velocity shows why speed alone cannot describe motion fully.
Vector field: A function assigning a vector to every point in a space. A single vector describes one quantity; a vector field describes its spatial distribution.
Euclidean vector: An element of Euclidean space represented by magnitude and direction, with components that transform under rotations. It is the familiar geometric model behind vectors such as displacement and force.
Rotation matrix: A matrix that represents a rotation while preserving lengths and angles. It changes vector components between rotated frames without changing the physical vector.

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