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

Toolbox:
• 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:
$\overrightarrow{OB}=\overrightarrow{OA}+\overrightarrow{AB}$
$\mid\overrightarrow{OB}\mid=\mid\overrightarrow{OA}\mid+\mid\overrightarrow{AB}\mid$
$\mid\overrightarrow{a}+\overrightarrow{b}\mid=\mid\overrightarrow{a}\mid+\mid\overrightarrow{b}\mid$
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.