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Let the position vectors of the points P, Q, R and S be \(\vec{a}=\overset{^}{i}+2\overset{^}{j}−5\overset{^}{k},\) \(\v…

Q1

Let the position vectors of the points P, Q, R and S be \(\vec{a}=\overset{^}{i}+2\overset{^}{j}−5\overset{^}{k},\) \(\vec{b}=3\overset{^}{i}+6\overset{^}{j}+3\overset{^}{k},\) \(\vec{c}=\frac{17}{5}\overset{^}{i}+\frac{16}{5}\overset{^}{j}+7\overset{^}{k}\) and \(\vec{d}=2\overset{^}{i}+\overset{^}{j}+\overset{^}{k},\) 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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