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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}\,

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}\,.

[Examples] [Links]

  automatically generated 3/28/2008