If \( \overrightarrow{\mathrm{OA}}=\overrightarrow{\mathrm{a}} ; \o...
If \( \overrightarrow{\mathrm{OA}}=\overrightarrow{\mathrm{a}} ; \overrightarrow{\mathrm{OB}}=\overrightarrow{\mathrm{b}} ; \overrightarrow{\mathrm{OC}}=2 \overrightarrow{\mathrm{a}}+3 \overrightarrow{\mathrm{b}}, \overrightarrow{\mathrm{OD}} \)
\( \mathrm{P} \)
W \( =\vec{a}-2 \vec{b} \), the length of \( \overline{\mathrm{OA}} \) is three times the length of \( \overrightarrow{\mathrm{OB}} \) and \( \overrightarrow{\mathrm{OA}} \) is perpendicular to \( \overrightarrow{\mathrm{DB}} \), then \( (\overrightarrow{\mathrm{BD}} \times \overrightarrow{\mathrm{AC}}) \cdot(\overrightarrow{\mathrm{OD}} \times \overrightarrow{\mathrm{OC}}) \) is
(1) \( 7|\vec{a} \times \vec{b}|^{2} \)
(2) \( 42|\vec{a} \times \vec{b}|^{2} \)
(3) 0
(4) 1
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