Let the position vectors of the points P, Q, R and S be a=i+2 j-5 k, b=3 i+6 j+3 k, c=17/5 i+16/5 j+7 k and d=2 i+j+k, respectively. Then which of the following statements is true?

(B) (b+2 d)/3 is the position vector of a point which divides P R internally in the ratio 5: 4

(A) The points P, Q, R and S are NOT coplanar

(C) (b+2 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 b × d is 95

Vector Algebra: JEE Advanced 2023 Mathematics question

JEE Advanced 2023 · JEE Adv 2023 Paper 2, Paper 2 · Q4

JEE Advanced 2023JEE Adv 2023 Paper 2, Paper 2MathematicsHardVector Algebra184× since 2002

Let the position vectors of the points

P, Q, R

and

S

\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?

JEE Advanced 2023 Vector Algebra Question with Answer (JEE Adv 2023 Paper 2 Paper 2, Q4) | JEE Arc

JEE Advanced 2023 · JEE Adv 2023 Paper 2, Paper 2 · Q4

JEE Advanced 2023JEE Adv 2023 Paper 2, Paper 2MathematicsHardVector Algebra184× since 2002

Let the position vectors of the points

P, Q, R

and

S

\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?