Let the position vectors of points P, Q, R and S be \overrightarrow{a}=\stackrel{\^}{i}+2 \stackrel{\^}{j}-5 \stackrel{\^}{k}, \overrightarrow{b}=3 \stackrel{\^}{i}+6 \stackrel{\^}{j}+3 \stackrel{\^}{k}, \overrightarrow{c}=\frac{17}{5} \stackrel{\^}{i}+\frac{16}{5} \stackrel{\^}{j}+7 \stackrel{\^}{k} and \overrightarrow{d}=2 \stackrel{\^}{i}+\stackrel{\^}{j}+\stackrel{\^}{k}, respectively. Then which of the following statements is true? [JEE Adv 2023 P2]

Correct Answer is : →b+2→d3 is the position vector of a point which divides PR internally in the ratio 5:4

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

\overrightarrow{{b}+2 \overrightarrow{d}}/{3} is the position vector of a point which divides P R internally in the ratio 5: 4

\overrightarrow{{b}+2 \overrightarrow{d}}/{3} is the position vector of a point which divides P R externally in the ratio 5: 4

The square of magnitude of the vector \overrightarrow{b} \times \overrightarrow{d} is 95

Vector Algebra

Section: Mathematics

Question : 7 of 38

Marks: +1, -0

Let the position vectors of points P,Q,R and S be

→

−5

→

=‌

+‌

and

→

, respectively. Then which of the following statements is true?

[JEE Adv 2023 P2]

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