CUET Mathematics - A vector of magnitude 8 units in the direction perpendicular to both the vectors i + j + k and 2i + k is | PYQs + Solutions

CUET Mathematics 2025 13 May Shift 2

Algebra

Medium

core

$8(\hat{i} + \hat{j} - 2\hat{k})$

$\frac{8}{\sqrt{6}}(-\hat{i} + \hat{j} + 2\hat{k})$

$\frac{8}{\sqrt{6}}(\hat{i} + \hat{j} - 2\hat{k})$

$\frac{8}{\sqrt{6}}(\hat{i} - \hat{j} + 2\hat{k})$

✅ Correct Option: 3

Related questions:

15 May Shift 1

The position vector of a point which divides the line joining the points with position vectors $(\hat{i} - 2\hat{j})$ and $(2\hat{i} + \hat{k})$ externally in the ratio 2:1, is

13 May Shift 2

Match List-I with List-II

List-I	List-II
(A) Angle between $\hat{i} - \hat{j}$ and $\hat{i} + \hat{j}$	(I) $\pi$
(B) Angle between $\hat{i} - \hat{j} + \hat{k}$ and $-\hat{i} + \hat{j} - \hat{k}$	(II) $\frac{3\pi}{4}$
(C) Angle between $\hat{i} + \hat{j}$ and $-\hat{i}$	(III) $\frac{\pi}{4}$
(D) Angle between $\hat{i} + \hat{k}$ and $\hat{k}$	(IV) $\frac{\pi}{2}$

Choose the correct answer from the options given below:

14 May Shift 2

Let $\vec{a} = \hat{i} + \hat{j}$ , $\vec{b} = \hat{i} - \hat{j}$ and $\vec{c} = \hat{i} + \hat{j} + \hat{k}$ . If $\vec{m}$ is a unit vector perpendicular to both the vectors $\vec{b}$ and $\vec{c}$ , then $|\vec{a}.\vec{m}|$ is equal to

CUET Mathematics 2025 13 May Shift 2 PYQs

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