If ` vec adot vec adot=0\ a n d\ vec adot vec b=0` what can you conclude about the vector ` vec b ?`

Explanation

Given: `vec{a} cdot vec{a}=0`


`Rightarrow|vec{a}|^{2}=0`


`Rightarrow|vec{a}|=0 ldots(1)`


Given: `vec{a} cdot vec{b}=0`


`Rightarrow|vec{a}||vec{b}| cos theta=0`……….[ where theta is the angle between `vec{a} { and } vec{b}`}


`Rightarrow 0|vec{b}| cos theta=0` ………{From equation (1)}


`Rightarrow 0=0`


So, it means that for any vector `vec{b}`, the given equation `vec{a} cdot vec{b}=0` is Required.