\( \begin{array}{ll}\text { Comprehension } & : \text { The points } A, B \text { and } C \text ...

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\( \begin{array}{ll}\text { Comprehension } & : \text { The points } A, B \text { and } C \text { with }\end{array} \) 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 \( O E \) and \( C D \) are mutually perpendicular, then which of the following will be necessarily true?
(a) \( |\vec{b}-\vec{a}|=|\vec{c}-\vec{a}| \)
(b) \( |\vec{b}-\vec{a}|=|\vec{b}-\vec{c}| \)
(c) \( |\vec{c}-\vec{a}|=|\vec{c}-\vec{b}| \)
(d) \( |\vec{b}-\vec{a}|=|\vec{c}-\vec{a}|=|\vec{b}-\vec{c}| \)
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