[b]uVectors in 2D[/u]/b

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} )

[b]uVectors in 3D[/u]/b

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} )

[b]uVectors[/u]/b

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