[b]uVector addition[/u]/b

bTriangle/b law for vector addition:

mtaimg/images/topics/10/10-107-1.png/mtaimg

(\overrightarrow{AB} + \overrightarrow{BC} = \overrightarrow{AC} )

If (\overrightarrow{AB} = \bold{a}), (\overrightarrow{BC} = \bold{b}) and (\overrightarrow{AC} = \bold{c}), then:

(\bold{a} + \bold{b} = \bold{c} )

bParallelogram/b law for vector addition:

mtaimg/images/topics/10/10-107-2.png/mtaimg

(\overrightarrow{AB} + \overrightarrow{BC} = \overrightarrow{AC} )

(\overrightarrow{BC} = \overrightarrow{AD} )

(\implies \bold{a} + \bold{b} = \overrightarrow{AC} )

In column vector form:

(\begin{pmatrix} p \ q \end{pmatrix} + \begin{pmatrix} r \ s \end{pmatrix} = \begin{pmatrix} p+r \ q+s \end{pmatrix} )

[b]uVector subtraction[/u]/b

Subtracting a vector is the equivalent of adding the reverse of a vector

(\bold{a} - \bold{b} = \bold{a} + (-\bold{b}) )

[b]uMultiplication by a scalar[/u]/b

(\lambda \begin{pmatrix} p \ q \end{pmatrix} = \begin{pmatrix} \lambda p \ \lambda q \end{pmatrix} )