If ` vec a\ a n d\ vec b` are mutually perpendicular unit vectors, write the value of `| vec a+ vec b|dot`

Explanation

Given: `vec{a} and vec{b}` are unit vectors and they are perpendicular.


`Rightarrow|vec{a}|=|vec{b}|=1 ; vec{a} cdot vec{b}=0 `…….(1)


so ,


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


`=1+1+2(0)` ……. [from equation(1)]


`=2 `


Hence, `|vec{a}+vec{b}|=sqrt{2}`