If `theta` is the angle between two vectors ` vec a\ a n d\ vec b ,\ t h e n\ vec adot vec bgeq0` only when `0

Explanation

Let `theta ` be the angle between two vectors `vec{a} and vec{b}`.

Then, without loss of generality `vec{a} and vec{b}` are non-zero vectors so that `|vec{a}| and |vec{b}|` are positive

It is known that `quad vec{a} cdot vec{b}=|vec{a}||vec{b}| cos theta`

`therefore vec{a} cdot vec{b} geq 0 `

`Rightarrow|vec{a}||vec{b}| cos theta geq 0 `

`Rightarrow cos theta geq 0 quad[|vec{a}| text { and }|vec{b}| text { are positive }] `

`Rightarrow 0 leq theta leq frac{pi}{2}`

Hence, `vec{a} cdot vec{b} geq 0 when 0 leq theta leq frac{pi}{2}`

...