Vectorcomponenten in het Cartesiaanse coördinatensysteem

The Cartesian coordinate system consists of three mutually perpendicular axes defined by unit vectors intersecting at the origin.

Unit vectors have unit magnitude and only point the direction.

For Cartesian systems, î, ĵ, and k̂ are the unit vectors along the positive x, y, and z axes, respectively.

In this frame, every vector is the sum of its orthogonal projections onto each of the axes. These projections are known as the vector components.

We write each vector component by its magnitude and a unit vector along the axis. The magnitudes represent the scalar components of the vector.

Thus, any vector is the vector sum of its components.

Using the scalar components, the magnitude of a vector is given by the square root of the sum of the squares of its components.

For a vector on a plane, its direction, which is the angle made by the vector with the positive x-axis in the anticlockwise direction, is the tan inverse of the y-component over the x-component.

Conversely, the x-component of a vector is the magnitude times the cosine of the angle made with the x-axis.

Its y-component is the magnitude times the sine of the angle made by the vector with the x-axis.