COMEDK 2026 Morning Shift | Vector Algebra Question 3 | Mathematics

Let $\vec{p}$ and $\vec{q}$ be the position vectors of P and Q with respect to the origin. If points R and S divide PQ internally and externally in the ratio 2:3 respectively, then $\overrightarrow{O R}$ and $\overrightarrow{O S}$ are perpendicular when

$4|\vec{p}|^2=9|\vec{q}|^2$

$9|\vec{p}|=4|\vec{q}|^2$

$9|\vec{p}|^2=4|\vec{q}|^2$

$4|\vec{p}|^2=9|\vec{q}|$

COMEDK 2025 Evening Shift

MCQ (Single Correct Answer)

-0

If $\vec{a}$ and $\vec{b}$ are two vectors such that $\vec{a} \cdot \vec{b}=|\vec{a} \times \vec{b}|$ then the angle between $\vec{a}$ and $\vec{b}$ is

$\frac{\pi}{4}$

$\pi$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

COMEDK 2025 Evening Shift

MCQ (Single Correct Answer)

-0

For any vector $\vec{p}$, the value of $\left[2\left\{|\vec{p} \times \hat{\imath}|^2+|\vec{p} \times \hat{\jmath}|^2+|\vec{p} \times \hat{k}|^2\right\}\right]$ is

$4|\vec{p}|^2$

$2|\vec{p}|^2$

$4|\vec{p}|$

$2|\vec{p}|$

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