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In linear algebra, a coordinate pair like $(3, -2)$ is viewed not just as a static location, but as scaling factors. The first number scales the horizontal unit vector $\hat{i}$, and the second scales the vertical unit vector $\hat{j}$.

Conditions: Working within a standard 2D Cartesian coordinate system; Using the standard unit basis vectors $\hat{i}$ and $\hat{j}$

In linear algebra, a coordinate pair like $(3, -2)$ is viewed not just as a static location, but as scaling factors. The first number scales the horizontal unit vector $\hat{i}$, and the second scales the vertical unit vector $\hat{j}$.

Conditions: Working within a standard 2D Cartesian coordinate system; Using the standard unit basis vectors $\hat{i}$ and $\hat{j}$

In a 2D plane, the first component dictates horizontal movement (right positive, left negative) and the second dictates vertical movement (up positive, down negative) from the origin to the tip.

Conditions: Standard Cartesian coordinate system; Vector anchored at the origin

In a 2D plane, the first component dictates horizontal movement (right positive, left negative) and the second dictates vertical movement (up positive, down negative) from the origin to the tip.

Conditions: Standard Cartesian coordinate system; Vector anchored at the origin