The projection of the vector $\vec{a} = \hat{i} + 2\hat{j} - 3\hat{k}$ on the vector $2\hat{i} + 6\hat{j} + 3\hat{k}$ is

Match List-I with List-II

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

Let $\vec{a}, \vec{b}$ be two vectors such that $|\vec{a}| = 2, |\vec{b}| = 3, \vec{a} \cdot \vec{b} = 4$, then $|\vec{a} - \vec{b}|$ is equal to

If $\vec a=\hat i+\hat j+2\hat k$ and $\vec b=2\hat i+\hat j+2\hat k$, then the unit vector in the direction of $2\vec a-\vec b$ is equal to :

The vectors from origin to the points A and B are $\vec{a}=2\hat{i}-3\hat{j}+2\hat{k}$ and $\vec{b}=2\hat{i}+3\hat{j}+\hat{k}$ respectively, then the area (in Sq. unit) of triangle OAB is:

If $\vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c}$, $\vec{a} \times \vec{b} = \vec{a} \times \vec{c}$ and $\vec{a} \neq {0}$, then the vector $\vec{b}$ in equal to.

The area of the parallelogram whose adjacent sides are determined by the vectors $\vec{a} = \hat{i} - \hat{j} + 3\hat{k}$ and $\vec{b} = 2\hat{i} - 7\hat{j} + \hat{k}$ is :