If a . a =0 and a . b =0, what can you conclude about the vector … - Vidyadip

Question

If $\vec{\text{a}}.\vec{\text{a}}=0$ and $\vec{\text{a}}.\vec{\text{b}}=0,$ what can you conclude about the vector $\vec{\text{b}}$?

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Answer

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

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