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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