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If \( \overrightarrow a \) x \( \overrightarrow b = \overrightarrow c \) x \( \overrightarrow d\) and \( \overrightarrow a\) x \( \overrightarrow c = \overrightarrow b \) x \( \overrightarrow d\) show that \( \overrightarrow a-\overrightarrow d\) is parallel to \( \overrightarrow b-\overrightarrow c\), where \( \overrightarrow a \neq \overrightarrow d\: and \: \overrightarrow b \neq \overrightarrow c.\)

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