Let $\vec{a} = 4\hat{i} - \hat{j} + 3\hat{k}$ and $\vec{b} = -2\hat{i} + \hat{j} - 2\hat{k}$. Then

(A) $\vec{a}$ is a unit vector

(B) $\vec{a} \times \vec{b} = -\hat{i} + 2\hat{j} + 2\hat{k}$

(C) $\vec{a}$ and $\vec{b}$ are parallel vectors

(D) $\vec{a}$ and $\vec{b}$ are neither parallel nor perpendicular vectors

Choose the correct answer from the options given below :

$[\vec{a} + \vec{b},\ \vec{b} + \vec{c}, \vec{a} + \vec{b} + \vec{c}]$ is equal to

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:

If $\vec{a}$ is a non-zero vector, then always

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

Match List-I with List-II

Let $\theta$ be the angle between the vectors $\vec{a}$ and $\vec{b}$.

If $\vec{a} = \hat{i} - \hat{j} + \hat{k}$, $\vec{b} = 2\hat{i} + \hat{j} - 3\hat{k}$, $\vec{c} = 2\hat{i} - \hat{j} + 7\hat{k}$ and $\vec{a} \times (\vec{b} \times \vec{c}) = \lambda \vec{b} + \mu \vec{c}$

(When $\lambda$, $\mu$ are scalars), then the value of $\lambda + \mu$ is: