Match List-I with List-II Let $\theta$ be the angle between the vectors $\vec{a}$ and $\vec{b}$. | List-I | List-II | | --- | --- | | (A) $\vec{a} \cdot \vec{b}$ | (I) $\dfrac{\vec{a} \cdot \vec{b}}{\vert \vec{b}\vert ^2} \vec{b}$ | | (B) $\vec{a} \times \vec{b}$ | (II) $\vec{a} \cdot \vec{b} = 0$ | | (C) Projection vector of $\vec{a}$ on $\vec{b}$ ($\ne{0}$) | (III) $\vert \vec{a}\vert \vert \vec{b}\vert \sin \theta \, \hat{n}$ where $\hat{n}$ is a unit vector perpendicular to both $\vec{a}$ and $\vec{b}$ | | (D) $\vec{a}$ and $\vec{b}$ are orthogonal vectors | (IV) $\vert \vec{a}\vert \vert \vec{b}\vert \cos \theta$ |

Correct Answer: C. (A) - (IV), (B) - (III), (C) - (I), (D) - (II)

Match List-I with List-II Let θ be the… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Algebra

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Match List-I with List-II

Let $\theta$ be the angle between the vectors $\vec{a}$ and $\vec{b}$ .

List-I	List-II
(A) $\vec{a} \cdot \vec{b}$	(I) $\dfrac{\vec{a} \cdot \vec{b}}{\vert \vec{b}\vert ^2} \vec{b}$
(B) $\vec{a} \times \vec{b}$	(II) $\vec{a} \cdot \vec{b} = 0$
(C) Projection vector of $\vec{a}$ on $\vec{b}$ ( $\ne{0}$ )	(III) $\vert \vec{a}\vert \vert \vec{b}\vert \sin \theta \, \hat{n}$ where $\hat{n}$ is a unit vector perpendicular to both $\vec{a}$ and $\vec{b}$
(D) $\vec{a}$ and $\vec{b}$ are orthogonal vectors	(IV) $\vert \vec{a}\vert \vert \vec{b}\vert \cos \theta$

Official previous-year question

Held on 29 May 2025 · Verified 13 Jul 2026.

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