JEE Math Practice Question

Let the position vectors of the points $P, Q, R$ and $S$ be $\vec{a}=\hat{i}+2 \hat{j}-5 \hat{k}, \vec{b}=3 \hat{i}+6 \hat{j}+3 \hat{k}$, $\vec{c}=\frac{17}{5} \hat{i}+\frac{16}{5} \hat{j}+7 \hat{k}$ and $\vec{d}=2 \hat{i}+\hat{j}+\hat{k}$, respectively. Then which of the following statements is true?

1. A.The points $P, Q, R$ and $S$ are NOT coplanar
2. B.$\frac{\vec{b}+2 \vec{d}}{3}$ is the position vector of a point which divides $P R$ internally in the ratio $5: 4$
3. C.$\frac{\vec{b}+2 \vec{d}}{3}$ is the position vector of a point which divides $P R$ externally in the ratio $5: 4$
4. D.The square of the magnitude of the vector $\vec{b} \times \vec{d}$ is 95