MYP Extended Mathematics Vector Representation Key Definitions

A vector written in component form as $\binom{x}{y}$, representing a translation of $x$ units horizontally and $y$ units vertically.

For a vector $\mathbf{a}$, the vector $-\mathbf{a}$ has the same magnitude but the opposite direction.

Two vectors that point in the same or opposite direction. Equivalently, one is a scalar multiple of the other.

The vector from the origin $O$ to a point, written $\overrightarrow{OA}$.

The single vector that has the same effect as performing several vectors in sequence, for example $\mathbf{a}+\mathbf{b}$.

A vector of the form $k\mathbf{a}$, where $k$ is a number (scalar). It is parallel to $\mathbf{a}$ and has magnitude $|k|\,|\mathbf{a}|$.

A quantity with both magnitude (size) and direction, often represented by a directed line segment (an arrow).