CUET Mathematics - If i,j and k are unit vectors along co-ordinates axes OX, OY and OZ respectively, then which of the following is/are true? (A) i x i = 0 (B) i x k = j (C) i * i = 1 (D) i * j = 0 Choose the correct answer from the options given below: | PYQs + Solutions

CUET Mathematics 2025 14 May Shift 1

Algebra

Medium

core

(A) and (B) only

(A), (C) and (D) only

(A) only

(A), (B), (C) and (D)

✅ Correct Option: 2

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If $\vec{a}$ , $\vec{b}$ and $\sqrt{3}\vec{a} - \vec{b}$ are three unit vectors, then the angle between $\vec{a}$ and $\vec{b}$ is:

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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) $\dfrac{\vec{a} \cdot \vec{b}}{\|\vec{b}\|^2} \vec{b}$
(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) $\|\vec{a}\|\|\vec{b}\| \sin \theta \, \hat{n}$ 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) $\|\vec{a}\|\|\vec{b}\| \cos \theta$

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If $\vec{a} = 3\hat{i} - 6\hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} - 4\hat{j} + 2\hat{k}$ are such that $\vec{a} \parallel \vec{b}$ , then $3\lambda + 2 =$

CUET Mathematics 2025 14 May Shift 1 PYQs

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