Definition:Vector Quantity/Component/Cartesian 3-Space

Definition
Let $\mathbf a$ be a vector quantity embedded in Cartesian $3$-space $S$.

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

Let $\mathbf i$, $\mathbf j$ and $\mathbf k$ be the unit vectors in the positive directions of the $x$-axis, $y$-axis and $z$-axis respectively.

Then:
 * $\mathbf a = a_1 \mathbf i + a_2 \mathbf j + a_3 \mathbf k$

where:
 * $a_1 \mathbf i$, $a_2 \mathbf j$ and $a_3 \mathbf k$ are the component vectors of $\mathbf a$ in the $\mathbf i, \mathbf j, \mathbf k$ directions
 * $a_1$, $a_2$ and $a_3$ are the components of $\mathbf a$ in the $\mathbf i$, $\mathbf j$ and $\mathbf k$ directions.