Coordinates of a vector
Vectors exist in a plane as well as in three-dimensional space. To easily represent them in the coordinate system, use the column vectors.
i
Info
Alongside column vectors row vectors exist, as well. These are usually not important at school.
Vectors in the plane
A vector in a plane looks as follows:
$\vec{v}=\begin{pmatrix}v_1\\v_2\end{pmatrix}$
The coordinates $v_1, v_2$ of the vector $\vec{v}$ show the shift along the coordinate axes.
Example
The illustrated vector $\vec{v}=\begin{pmatrix}\color{green}{3}\\\color{red}{2}\end{pmatrix}$ has a shift by $\color{green}{+3}$ in the x-direction and $\color{red}{+2}$ in the y-direction
Vectors in space
Vectors are also available in three-dimensional space. Logically they have one more coordinate.
$\vec{v}=\begin{pmatrix}v_1\\v_2\\v_3\end{pmatrix}$
