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Vector Algebra question

2023 · Shift 2 · Q21

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PYQ Library
JEE Advanced
Mathematics
Vector Algebra
2023 · Shift 2 · Q21

Vector Algebra question

2023 · Shift 2 · Q21

JEE AdvancedMathematicsVector AlgebraMCQ+3 / −1

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

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