The resultant of $\vec{A} \times 0$ will be equal to

If $|A|=2, |B|=5$ and $|A \times B|=8$. If the angle between $A$ and $B$ is acute,then $A \cdot B$ is

Two adjacent sides of a parallelogram are represented by the two vectors $\hat{i} + 2\hat{j} + 3\hat{k}$ and $3\hat{i} - 2\hat{j} + \hat{k}$. What is the area of the parallelogram?

If $\overrightarrow{A} = (2\hat{i} + 3\hat{j} - \hat{k}) \; m$ and $\overrightarrow{B} = (\hat{i} + 2\hat{j} + 2\hat{k}) \; m$,the magnitude of the component of vector $\overrightarrow{A}$ along vector $\overrightarrow{B}$ will be $...... \; m$.

Three vectors $\vec a$,$\vec b$,and $\vec c$ satisfy the relations $\vec a \cdot \vec b = 0$ and $\vec a \cdot \vec c = 0$. The vector $\vec a$ is parallel to:

If $\vec{A} \times \vec{B} = \vec{0}$ and $\vec{B} \times \vec{C} = \vec{0}$,what is the angle between $\vec{A}$ and $\vec{C}$?