CUET Mathematics 2022 17 Aug Shift 2 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:

The vector in the direction of the vector $2\hat{i} - \hat{j} - 2\hat{k}$ that has magnitude 9 units is:

Let $\vec{a} = 2\hat{i} - \hat{j}, \vec{b} =- 4\hat{j} + k\,\text{and}\,\vec{c} = \hat{i} + 2\hat{k}$. If $\vec{d}$ is a vector perpendicular to both $\vec{a}$ and $\vec{b}$ such that $\vec{c} \cdot \vec{d} = 34$, then $|\vec{d}|$ is equal to