If \( \vec{a}=\vec{b}+\vec{c}, \vec{b} \times \vec{d}=\overrightarrow{0} \) and \( \vec{c} \cdot...

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If \( \vec{a}=\vec{b}+\vec{c}, \vec{b} \times \vec{d}=\overrightarrow{0} \) and \( \vec{c} \cdot \vec{d}=\overrightarrow{0} \), then \( \frac{\vec{d} \times(\vec{a} \times \vec{d})}{\vec{d}^{2}} \) is equal to
(a) \( \vec{a} \)
(b) \( \vec{b} \)
(c) \( \vec{c} \)
(d) \( \vec{d} \)
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