Question

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

Answer 1

It is given that $\vec{a}.\vec{a}=0 \space and \space \vec{a}.\vec{b}=0$
Now,
$\vec{a}.a=0⇒ |\vec{a}|^{2}=0⇒|\vec{a}|=0$
$∴\vec{a}$ is a zero vector.
Hence,vector $\vec{b}$ satisfying $\vec{a}.\vec{b}=0$ can be any vector.