CUET Mathematics - The projection of the vector a = i + 2j - 3k on the vector 2i + 6j + 3k is | PYQs + Solutions

CUET Mathematics 2025 13 May Shift 1

Algebra

Medium

core

$\frac{5}{\sqrt{14}}$

$\frac{5}{7}$

$\frac{5}{14}$

✅ Correct Option: 2

Related questions:

21 May Shift 2

If $\vec{a}$ and $\vec{b}$ are two non-zero vectors such that $|\vec{a} \cdot \vec{b}| = |\vec{a} \times \vec{b}|$ , then the angle $\theta$ between $\vec{a}$ and $\vec{b}$ is

21 May Shift 1

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:

21 May Shift 1

Match List-I with List-II

List-I	List-II
(A) The vectors $\vec{a}$ = $\hat{i} + \hat{j} + 2\hat{k}$ and $\vec{i} + \lambda\hat{j} + \hat{k}$ are perpendicular if λ is equal to	(I) 1
(B) The vectors $3\hat{i} + q\hat{j} - \hat{k}$ and $2\hat{i} + \hat{j} - \hat{k}$ 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 $\vec{b}$ = $3\hat{i} - \hat{j} + \hat{k}$ is	(III) 2/3
(D) If $\\|\vec{a}\\|$ = 1 and $\vec{a}\cdot\vec{b}$ = 0, then $\\|\vec{a}\\|$ is equal to	(IV) 2

Choose the correct answer from the options given below:

CUET Mathematics 2025 13 May Shift 1 PYQs

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