\( \begin{array}{ll}\text { Comprehension } & : \text { The points } A, B \text { and } C \text ... VIDEO
\( \begin{array}{ll}\text { Comprehension } & : \text { The points } A, B \text { and } C \text { with }\end{array} \) position vectors \( \vec{a}, \vec{b} \& \vec{c} \) and respectively lie on a circle centred at origin \( O \). Let \( G \) and \( E \) be the centroid of \( \triangle A B C \) and \( \triangle A C D \) respectively where \( D \) is midpoint of \( A B \).
If \( [\overrightarrow{A B} \overrightarrow{A C} \overrightarrow{A B} \times \overrightarrow{A C}]=\lambda[\overrightarrow{A E} \overrightarrow{A G} \overrightarrow{A E} \times \overrightarrow{A G}] \), then the value of \( \lambda \) is:
(a) -18
(b) 18
(c) -324
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