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

CUET Mathematics 2025 21 May Shift 1

Algebra

Medium

core

$\frac{\pi}{6}$

$\frac{\pi}{4}$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

✅ Correct Option: 1

Related questions:

27 May Shift 1

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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3 June Shift 1

The projection of the vector $2\hat{i} - \hat{j} + 3\hat{k}$ on the vector $3\hat{i} + 2\hat{j} + 6\hat{k}$ is

27 May Shift 1

Which of the following statements are true?

(A) The vector joining the points P(2, 3, 0) and Q(-1,-2,-4) directed from P to Q is $\vec{PQ} = -3\hat{i} - 5\hat{j} - 4\hat{k}$

(B) Projection of a vector $\vec{a}$ on other vector $\vec{b}$ is $\frac{\vec{a}.\vec{b}}{|\vec{a}|}$

(C) If $\vec{a} = \hat{i} - 2\hat{j} + \hat{k}$ and $\vec{b} = -2\hat{i} + 4\hat{j} + 5\hat{k}$ then $\vec{a} + \vec{b} = -\hat{i} + 2\hat{j} + 6\hat{k}$

(D) If $\theta$ is the angle between $\vec{a}$ and $\vec{b}$ then $\cos \theta = \frac{\vec{a}.\vec{b}}{|\vec{a}||\vec{b}|}$

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CUET Mathematics 2025 21 May Shift 1 PYQs

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