CUET Mathematics - If a, b and sqrt(3)a + b are unit vectors, then the angle between a and b is: | PYQs + Solutions

CUET Mathematics 2025 26 May Shift 2

Algebra

Medium

core

$\frac{\pi}{2}$

$\frac{\pi}{3}$

$\frac{\pi}{6}$

$\frac{5\pi}{6}$

✅ Correct Option: 4

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If $\vec{a}$ is any vector, then $|\vec{a} \times \hat{i}|^2 + |\vec{a} \times \hat{j}|^2 + |\vec{a} \times \hat{k}|^2$ is equal to

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Match List-I with List-II

List-I	List-II
(A) If vector $\vec{a}$ and $\vec{b}$ are such that $\vec{a} = \lambda \vec{b}$ and $\|\vec{a}\| = \|\vec{b}\|$ , then	(I) $\vec{a}$ and $\vec{b}$ are orthogonal
(B) Projection vector of $\vec{a}$ on $\vec{b}$	(II) $[0, 12]$
(C) $\vec{a}$ and $\vec{b}$ are non-zero vectors such that $\|\vec{a} + \vec{b}\| = \|\vec{a} - \vec{b}\|$ , then	(III) $\vec{a} = \pm \vec{b}$
(D) If $\|\vec{a}\| = 4, -3 \le \lambda \le 2$ , then the range of $\|\lambda \vec{a}\|$	(IV) $(\dfrac{\vec{a} \cdot \vec{b}}{\|\vec{b}\|^2}) \vec{b}$

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CUET Mathematics 2025 26 May Shift 2 PYQs

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