Match **List - I** with **List - II**. | | List - I | | List - II | |---|---|---|---| | (A) | Area of triangle $\Delta$ with adjacent sides $\vec{a}$ and $\vec{b}$ | (I) | $\vec{a} \times \vec{b}$ | | (B) | Area of parallelogram with adjacent sides $\vec{a}$ and $\vec{b}$ | (II) | $\frac{1}{2}\lvert \vec{a} \times \vec{b} \rvert$ | | (C) | $(\vec{a} - \vec{b}) \times (\vec{a} + \vec{b})$ | (III) | $\lvert \vec{a} \times \vec{b} \rvert$ | | (D) | $\lvert \vec{a} \rvert \lvert \vec{b} \rvert \sin\theta \hat{n}$, where symbols have their usual meaning | (IV) | $2(\vec{a} \times \vec{b})$ | Choose the **correct** answer from the options given below :

(A) Area of triangle $=\frac{1}{2}|\vec{a}\times\vec{b}|$, II. (B) Area of parallelogram $=|\vec{a}\times\vec{b}|$, III. (C) $(\vec{a}-\vec{b})\times(\vec{a}+\vec{b})=2(\vec{a}\times\vec{b})$, IV. (D) $|\vec{a}||\vec{b}|\sin\theta\,\hat{n}=\vec{a}\times\vec{b}$, I.

Match List - I with List - II. | | List - I | | List - II | |---|---|---|---| | (A) | Area of triangle Δ… - CUET UG 2023 Mathematics PYQ

CUET UG 2023 — Mathematics Algebra

2023mcqmedium

Match List - I with List - II.

	List - I		List - II
(A)	Area of triangle $\Delta$ with adjacent sides $\vec{a}$ and $\vec{b}$	(I)	$\vec{a} \times \vec{b}$
(B)	Area of parallelogram with adjacent sides $\vec{a}$ and $\vec{b}$	(II)	$\frac{1}{2}\lvert \vec{a} \times \vec{b} \rvert$
(C)	$(\vec{a} - \vec{b}) \times (\vec{a} + \vec{b})$	(III)	$\lvert \vec{a} \times \vec{b} \rvert$
(D)	$\lvert \vec{a} \rvert \lvert \vec{b} \rvert \sin\theta \hat{n}$ , where symbols have their usual meaning	(IV)	$2(\vec{a} \times \vec{b})$

Choose the correct answer from the options given below :

Official previous-year question

Held on 22 May 2023 · Verified 13 Jul 2026.

Options

A
(A)-(III), (B)-(IV), (C)-(I), (D)-(II)
B
(A)-(IV), (B)-(I), (C)-(III), (D)-(II)
C
(A)-(II), (B)-(III), (C)-(IV), (D)-(I)
D
(A)-(II), (B)-(IV), (C)-(III), (D)-(I)

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Solution

(A) Area of triangle $=\frac{1}{2}|\vec{a}\times\vec{b}|$ , II.

(B) Area of parallelogram $=|\vec{a}\times\vec{b}|$ , III.

(D) $|\vec{a}||\vec{b}|\sin\theta\,\hat{n}=\vec{a}\times\vec{b}$ , I.

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