Three vectors \(\vec{a}, \vec{b}\) and \(\vec{c}\) in \(\mathbb{R}^{3}\) satisfy the following equation.
\[ \vec{a} \cdot \vec{b} = \vec{c} \cdot \vec{b} \]
What can you deduce about \(\vec{a}\) and \(\vec{c}\) from this information?

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