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For two non zero vectors $ \overrightarrow a \: and \: \overrightarrow b$ write when $ |\overrightarrow a+\overrightarrow b | = | \overrightarrow a | + | \overrightarrow b | $

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  • Two or more vectors are said to be collinear if their magnitudes are equal or proportional.
Step 1:
$\mid\overrightarrow{a}+\overrightarrow {b}\mid=\mid\overrightarrow a\mid+\mid\overrightarrow b\mid$
When $ \overrightarrow a,\overrightarrow b$ are collinear vectors,
Let $\overrightarrow{OA}=\overrightarrow a,\overrightarrow{AB}=\overrightarrow b$ then
$\overrightarrow a+\overrightarrow b=\overrightarrow {OA}+\overrightarrow{AB}=\overrightarrow{OB}$
Step 2:
Hence when $\overrightarrow{a}$ and $\overrightarrow{b}$ are collinear vectors.
$\mid\overrightarrow{a}+\overrightarrow {b}\mid=\mid\overrightarrow a\mid+\mid\overrightarrow b\mid$
Hence proved.
answered Nov 8, 2013 by sreemathi.v

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