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The value of expression \( [\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{d}} \overrightarrow{\mathbf{e}} \times \overrightarrow{\mathbf{f}}] \) is equal to :
(a) \( [\overrightarrow{\mathbf{a}} \overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{d}}][\overrightarrow{\mathbf{c}} \overrightarrow{\mathbf{e}} \overrightarrow{\mathbf{f}}]-[\overrightarrow{\mathbf{a}} \mathbf{b} \overrightarrow{\mathbf{c}}][\overrightarrow{\mathbf{d}} \overrightarrow{\mathbf{e}} \overrightarrow{\mathbf{f}}] \)
(b) \( [\overrightarrow{\mathbf{a}} \overrightarrow{\mathbf{b}} \mathbf{e}][\overrightarrow{\mathbf{f}} \overrightarrow{\mathbf{c}} \overrightarrow{\mathbf{d}}]-[\overrightarrow{\mathbf{a}} \overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{f}}][\overrightarrow{\mathbf{e}} \mathbf{\mathbf { c }} \overrightarrow{\mathbf{d}}] \)
\( \mathrm{P} \)
(c) \( [\overrightarrow{\mathbf{c}} \overrightarrow{\mathbf{d}} \overrightarrow{\mathbf{a}}][\overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{e}} \overrightarrow{\mathbf{f}}]-[\overrightarrow{\mathbf{c}} \mathbf{\mathbf { d }} \overrightarrow{\mathbf{b}}][\overrightarrow{\mathbf{a}} \mathbf{\mathbf { e }} \overrightarrow{\mathbf{f}}] \)
(d) \( [\overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{c}} \mathbf{\mathbf { d }}][\overrightarrow{\mathbf{a}} \mathbf{\mathbf { e }} \overrightarrow{\mathbf{f}}]-[\overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{c}} \overrightarrow{\mathbf{f}}][\overrightarrow{\mathbf{a}} \mathbf{e} \overrightarrow{\mathbf{d}}] \)
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