Vector Algebra · JEE Advanced previous year questions

2023 1 question

1. Q42023 · 4 Jun 2023 · Paper 2

   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 $PR$ internally in the ratio $5:4$
   3. C.$\frac{\vec{b}+2\vec{d}}{3}$ is the position vector of a point which divides $PR$ externally in the ratio $5:4$
   4. D.The square of the magnitude of the vector $\vec{b}\times \vec{d}$ is 95
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   Answer: B