Vector addition

Vector addition combines vectors by adding their corresponding components. The result is a vector whose magnitude and direction depend on the vectors being added.

Component form: A representation of a vector by its scalar components along chosen coordinate axes. Adding components axis by axis gives the sum directly in coordinates.
Vector: A quantity or mathematical object with components that may represent magnitude and direction. Vector addition acts on these objects and returns another vector.
Displacement: A vector describing the change in position from an initial point to a final point. Successive displacements add to give the net change in position.
Scalar multiplication: An operation that multiplies a vector by a scalar, scaling its magnitude and possibly reversing its direction. It changes one vector by a number rather than combining two vectors.
Parallelogram law: A geometric rule in which two vectors from a common origin sum to the parallelogram's diagonal. It constructs the same resultant as component-wise addition.
Scalar: A quantity represented by a single number rather than a direction-bearing vector. Unlike scalar addition, vector addition must combine directional components.
Velocity: The rate of change of position, represented by a vector with magnitude and direction. Relative and combined motions are calculated by adding velocity vectors.
Vector subtraction: The operation of adding the additive inverse of one vector to another. Subtraction reverses one addend before applying the addition rule.
Triangle law of vector addition: A geometric construction that places the tail of one vector at the head of another to find their sum. It displays addition as a head-to-tail displacement.
Coordinate system: A framework of axes and rules for assigning coordinates to points or vectors. Components used in coordinate addition depend on the chosen axes.

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