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Let vectors \( \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d} \) be such that \( (\vec{a} \times \vec{b}) \times(\vec{c} \times \vec{d})=\overrightarrow{0} \). Let \( P_{1} \) and \( P_{2} \) be planes determined by the pairs of vectors \( \vec{a}, \vec{b} \) and \( \vec{c}, \vec{d} \), respectively. Then the angle between \( P_{1} \) and \( P_{2} \) is
(A) \( \pi / 4 \)
(B) \( \pi / 3 \)
(C) \( \pi / 2 \)
(D) undefined
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