Question

If $\overrightarrow{a.}\overrightarrow{a}=0$ and $\overrightarrow{a.}\overrightarrow{b}=0$ then what can be concluded about the vector $\overrightarrow{b}$ ?

Answer 1

If $\overrightarrow{a}.\overrightarrow{a}=0$

$\Rightarrow \left|a\right|.\left|a\right|\cos 0=0$

$\Rightarrow {\left|a\right|}^2=0$

$\therefore \left|a\right|=0$

$\therefore \overrightarrow{a}$ is a null vector =$0$

and hence, dot product of $\overrightarrow{a}$ with any other vector will always be zero

Hence $\overrightarrow{b}$ can be any vector