If $\overrightarrow A = 3\hat i + \hat j + 2\hat k$ and $\overrightarrow B = 2\hat i - 2\hat j + 4\hat k$,then the value of $|\overrightarrow A \times \overrightarrow B |$ will be:

The area of the parallelogram having diagonals $\vec{d_1} = 3\hat{i} + \hat{j} - 2\hat{k}$ and $\vec{d_2} = \hat{i} - 3\hat{j} + 4\hat{k}$ is:

The edges of a parallelepiped are represented by the vectors $\hat{i} + 2\hat{j}$,$4\hat{j}$,and $\hat{j} + 3\hat{k}$. Find its volume.

If $\overrightarrow{A} = 2\hat{i} + 3\hat{j} - \hat{k}$ and $\overrightarrow{B} = -\hat{i} + 3\hat{j} + 4\hat{k}$,then the projection of $\overrightarrow{A}$ on $\overrightarrow{B}$ will be:

Vector $\vec{A}$ of magnitude $5 \sqrt{3}$ units,another vector $\vec{B}$ of magnitude $10$ units are inclined to each other at an angle of $30^{\circ}$. The magnitude of the vector product of the two vectors is $\left[\sin 30^{\circ}=\frac{1}{2}\right]$

If $\overrightarrow{P} \cdot \overrightarrow{Q} = PQ,$ then the angle between $\overrightarrow{P}$ and $\overrightarrow{Q}$ is ....... $^\circ$.