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If $\vec{a} \cdot \vec{a}=0$ and $\vec{a} \cdot \vec{b}=0$, then what can be concluded about the vector $\vec{b}$ ?
Solution:
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Verified Answer
$\vec{a} \cdot \vec{a}=0$ and $\vec{a} \cdot \vec{b}=0$,
$$
\Rightarrow \quad \vec{a}=0
$$
Hence $b$ is any vector.
$$
\Rightarrow \quad \vec{a}=0
$$
Hence $b$ is any vector.
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