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}…

The points \(P, Q, R\) and \(S\) are NOT coplanar

\(\frac{\vec{b}+2 \vec{d}}{3}\) is the position vector of a point which divides PR internally in the ratio \(5: 4\)

\(\frac{\vec{b}+2 \vec{d}}{3}\) is the position vector of a point which divides PR externally in the ratio \(5: 4\)

The square of the magnitude of the vector \(\vec{b} \times \vec{d}\) is 95