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} cdot vec{b} `


`Rightarrow 4 vec{a} cdot vec{b}=0 `


`Rightarrow vec{a} cdot vec{b}=0 `


`Rightarrow vec{a} and vec{b}` are perpendicular.