CUET Mathematics - If a is a unit vector perpendicular to both the vectors b = j + 2k and c = i + 2j, then a is equal to | PYQs + Solutions

CUET Mathematics 2025 14 May Shift 2

Algebra

Medium

core

$\frac{-4\hat{i} + 2\hat{j} + \hat{k}}{\sqrt{21}}$

$\frac{4\hat{i} + 2\hat{j} - \hat{k}}{\sqrt{21}}$

$\frac{-4\hat{i} + 2\hat{j} - \hat{k}}{\sqrt{21}}$

$\frac{-4\hat{i} - 2\hat{j} - \hat{k}}{\sqrt{21}}$

✅ Correct Option: 3

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The angle between two lines whose direction ratios are propotional to $1,1,-2$ and $(\sqrt{3}-1),(-\sqrt{3}-1),-4$ is :

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

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Match List-I with List-II

List-I	List-II
(A) The vectors $\lambda\hat{i}$ $+ \hat{j} + 2\hat{k}$ and $\vec{i} + \lambda\hat{j} + \hat{k}$ are perpendicular if λ is equal to	(I) 1
(B) The vectors $3\hat{i} + 6\hat{j} - \hat{k}$ and $2\hat{i} + 4\hat{j} - \lambda\hat{k}$ are collinear if λ is equal to	(II) -1
(C) The number of vectors of unit-length which are perpendicular to both the vectors $\vec{a}$ = $\hat{i} + \hat{j} + 2\hat{k}$ and $\vec{b}$ = $3\hat{i} - \hat{j} + 5\hat{k}$ is	(III) 2/3
(D) If $\\|\vec{a}\\|$ = 1 and $\vec{a} +\vec{b}$ = $\vec0,$ then $\\|\vec{b}\\|$ is equal to	(IV) 2

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CUET Mathematics 2025 14 May Shift 2 PYQs

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