For any two vectors ` vec a\ a n d\ vec b` write when `| vec a+ vec b|=| vec a|+| vec b|` holds.

Explanation

Given: `|vec{a}+vec{b}|=|vec{a}|+|vec{b}|`


Squaring both sides of equation,


`|vec{a}+vec{b}|^{2}=(|vec{a}|+|vec{b}|)^{2} `


`Rightarrow|vec{a}|^{2}+|vec{b}|^{2}+2 vec{a} cdot vec{b}=|vec{a}|^{2}+|vec{b}|^{2}+2|vec{a}||vec{b}|`


`Rightarrow vec{a} cdot vec{b}=|vec{a}||vec{b}|`


`Rightarrow|vec{a}||vec{b}| cos theta=|vec{a}||vec{b}|` ………….{ where `theta` is the angle between `vec{a} and vec{b}`}


`Rightarrow cos theta=1`


`Rightarrow theta=0^{circ} `


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