CUET Mathematics 2026 19th May Shift 1 PYQs

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

Choose the correct answer from the options given below:

If $\vec{a}=2\hat{i}+\hat{j}$, and $\vec{b}=\hat{j}-\hat{k}$, then which of the following statements is/are TRUE ?

A. $|\vec{a}+\vec{b}|=3$

B. Unit vector along $\vec{a}+\vec{b}$ is $2\hat{i}+2\hat{j}-\hat{k}$

C. Direction ratio of $\vec{a}+\vec{b}$ are 2, 2, -1

D. unit vector perpendicular to $\vec{a}$ and $\vec{b}$ is $-\frac{1}{3}\hat{i}+\frac{2}{3}\hat{j}+\frac{2}{3}\hat{k}$

Choose the correct answer from the options given below:

If $\vec{p} = \hat{i} + \hat{j} - 2\hat{k}$ and $\vec{q} = 2\hat{i} + \hat{j} - \hat{k}$, then the area of parallelogram having diagonals $(\vec{p} + \vec{q})$ and $(\vec{p} - \vec{q})$ is