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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{…

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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?

a

The points P, Q, R and S are not coplanar

b

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

c

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

d

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

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