CUET Mathematics - The value of , for which the two vectors 2i - j + 2k and 3i + + k are perpendicular, is: | PYQs + Solutions

15 May Shift 1

If $\vec{a} = 2\hat{i} - \hat{j} + 3\hat{k}$ and $\vec{b} = 2\hat{i} + 2\hat{j} + \hat{k}$ , then

Match List-I with List-II

List-I	List-II
(A) Projection of $\vec{a}$ on $\vec{b}$ is	(I) $-7\hat{i} + 4\hat{j} + 6\hat{k}$
(B) $\vec{a} imes \vec{b}$ is	(II) $\frac{1}{\sqrt{101}}(-7\hat{i} + 4\hat{j} + 6\hat{k})$
(C) unit vector along $\vec{a} + \vec{b}$ is	(III) $\frac{5}{3}$
(D) Unit vector perpendicular to both $\vec{a}$ & $\vec{b}$ is	(IV) $\frac{1}{\sqrt{33}}(4\hat{i} + \hat{j} + 4\hat{k})$

Choose the correct answer from the options given below:

14 May Shift 1

If $\hat{i},\hat{j}$ and $\hat{k}$ are unit vectors along co-ordinates axes OX, OY and OZ respectively, then which of the following is/are true?

(A) $\hat{i} \times \hat{i} = \vec{0}$

(B) $\hat{i} \times \hat{k} = \hat{j}$

(C) $\hat{i} \cdot \hat{i} = 1$

(D) $\hat{i} \cdot \hat{j} = 0$

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13 May Shift 2

The length of line segment joining the points with position vectors $2\hat{i} - 2\hat{j} + 3\hat{k}$ and $5\hat{i} + 2\hat{j} + 3\hat{k}$ is

CUET Mathematics 2025 2 June Shift 1 PYQs