Vectors in 2D

2D vectors can be represented as column vectors or using the unit vectors \(\bold{i}\) and \(\bold{j}\).

The unit vectors along the \(x\)- and \(y\)-axis are denoted by \(\bold{i}\) and \(\bold{j}\) respectively.

\(\bold{i} = \begin{pmatrix} 1 \\ 0 \end{pmatrix} \quad \bold{j} = \begin{pmatrix} 0 \\ 1 \end{pmatrix} \)

\(x\bold{i} + y\bold{j} = \begin{pmatrix} x \\ y \end{pmatrix} \)

Vectors in 3D

3D vectors can be represented as column vectors or using the unit vectors \(\bold{i}\), \(\bold{j}\) and \(\bold{k}\).

The unit vectors along the \(x\)-, \(y\)- and \(z\)-axis are denoted by \(\bold{i}\), \(\bold{j}\) and \(\bold{k}\) respectively.

\(\bold{i} = \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} \quad \bold{j} = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix} \quad \bold{k} = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \)

\(x\bold{i} + y\bold{j} + z\bold{k} = \begin{pmatrix} x \\ y \\ z \end{pmatrix} \)