Let $\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} - \hat{j} + 2\hat{k}$ be two vectors. Then which of the following are TRUE?

A. $\vec{a}$ and $\vec{b}$ are perpendicular

B. Projection of $\vec{a}$ on $\vec{b}$ is 1

C. $|\vec{a} \times \vec{b}| = 3\sqrt{13}$

D. $\vec{a} - \vec{b}$ is a unit vector

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If $\vec{a}$ and $\vec{b}$ are two perpendicular vectors such that $|\vec{a}| = 3$, $|\vec{b}| = 4$ and $\theta$ is the angle between $\vec{a}$ and $(\vec{a} - \vec{b})$, then $\cos\theta$ is equal to:

If $\vec{a}, \vec{b}, \vec{c}$ are three mutually perpendicular unit vectors, then $|\vec{a} + \vec{b} + \vec{c}|$ is equal to

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

If $\vec{a} = 2\hat{i} + \hat{j}$ and $\vec{b} = \hat{j} - \hat{k}$, then Match List-I with List-II

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A vector of magnitude 9, which is perpendicular to both the vectors $4\hat{i}-\hat{j}+3\hat{k}$ and $-2\hat{i}+\hat{j}-2\hat{k}$ is:

If $\theta$ is an acute angle and the vector $\vec{a} = (\sin \theta)\vec{i} + (\cos\theta)\vec{j}$ is perpendicular to the vector $\vec{b} = i - \sqrt{3}j$ then $\theta$ is equal to