CUET Mathematics 2023 15 June Shift 2 PYQs

If $\vec{a} = 2\hat{i} + m\hat{j} - n\hat{k}$ and $\vec{b} = l\hat{i} - 3\hat{j} + 4\hat{k}$ such that $\vec{a} = 2\vec{b}$ then the value of $14{l} + m + n$ is:

Let $\vec{OA} = 2\hat{i} - \hat{j} + \hat{k}$ and $\vec{OB} = \hat{i} + \hat{j} - \hat{k}$. Then

A. The magnitude of vector $\vec{OA}$ is 6

B. The magnitude of vector $\vec{OB}$ is $\sqrt{3}$

C. The vector $\vec{AB}$ is $(-\hat{i} + 2\hat{j} - 2\hat{k})$

D. $\vec{OA} \cdot \vec{OB} = 0$

E. $\vec{OA} \parallel \vec{OB}$

Choose the correct answer from the options given below:

If $\vec{a}$ and $\vec{b}$ are two non-zero orthogonal vectors, then $|\vec{a} + \vec{b}|$ is equal to