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Let \( A(3,0,-1), B(2,10,6) \) and \( C(1,2,1) \) be the vertices of a triangle and \( M \) be the mid-point of \( A C \). If \( G \)
\( \mathrm{P} \) divides \( B M \) in the ratio \( 2: 1 \), then \( \cos (\angle G O A)(O \)

W being the origin) is equal to
(2019 Main, 10 April I)
(a) \( \frac{1}{\sqrt{15}} \)
(b) \( \frac{1}{2 \sqrt{15}} \)
(c) \( \frac{1}{\sqrt{30}} \)
(d) \( \frac{1}{6 \sqrt{10}} \)
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