Category:Examples of Components of Vectors

This category contains examples of Component of Vector.

Let $\mathbf a$ be a vector quantity embedded in an $n$-dimensional Cartesian coordinate system $C_n$.

Let $\mathbf a$ be represented with its initial point at the origin of $C_n$.

Let $\mathbf e_1, \mathbf e_2, \ldots, \mathbf e_n$ be the unit vectors in the positive direction of the coordinate axes of $C_n$.

Then:

$\mathbf a = a_1 \mathbf e_1 + a_2 \mathbf e_2 + \cdots + a_3 \mathbf e_n$

where:

$a_1 \mathbf e_1, a_2 \mathbf e_2, \ldots, a_3 \mathbf e_n$ are the component vectors of $\mathbf a$ in the directions of $\mathbf e_1, \mathbf e_2, \ldots, \mathbf e_n$

$a_1, a_2, \ldots, a_3$ are the components of $\mathbf a$ in the directions of $\mathbf e_1, \mathbf e_2, \ldots, \mathbf e_n$.

The number of components in $\mathbf a$ is determined by the number of dimensions in the Cartesian coordinate system of its frame of reference.