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Mathematics-Online lexicon:

Addition of Vectors

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The sum of two vectors corresponds to the composition of two translations:

$\displaystyle \overrightarrow{PR} = \overrightarrow{PQ} + \overrightarrow{QR}\, . $

\includegraphics[width=7.4cm]{a_vec_addition}
Correspondingly for the coordinates, we have

$\displaystyle \vec{c} = \vec{a} + \vec{b} = \left(\begin{array}{c} a_1\\ a_... ... = \left(\begin{array}{c} a_1+b_1\\ a_2+b_2\\ a_3+b_3 \end{array}\right) . $


The translation opposite to $ \overrightarrow{PQ}$ is denoted by

$\displaystyle \overrightarrow{QP} = -\overrightarrow{PQ}\,. $

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  automatically generated 3/28/2008