Let the position vectors of points \(P, Q, R\) and \(S\) be
\[
\vec a = \hat i + 2\hat j - 5\hat k,\quad
\vec b = 3\hat i + 6\hat j + 3\hat k,\quad
\vec c = \frac{17}{5}\hat i + \frac{16}{5}\hat j + 7\hat k,\quad
\vec d = 2\hat i + \hat j + \hat k.
\]
Then which of the following statements is true?
(A) The points \(P, Q, R, S\) are not coplanar. (B) \(\displaystyle \frac{\vec b + 2\vec d}{3}\) divides \(PR\) internally in the ratio \(5:4\). (C) \(\displaystyle \frac{\vec b + 2\vec d}{3}\) divides \(PR\) externally in the ratio \(5:4\). (D) The square of magnitude of \(\vec b \times \vec d\) is \(95\).