The dot product of two mutually perpendicular vectors is:

If $\vec{A}, \vec{B}$ and $\vec{C}$ are vectors having unit magnitude. If $\vec{A} + \vec{B} + \vec{C} = \vec{0}$,then $\vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{C} + \vec{C} \cdot \vec{A}$ will be:

Find the unit vector perpendicular to $\vec{A}$ and $\vec{B}$ where $\vec{A} = \hat{i} - 2\hat{j} + \hat{k}$ and $\vec{B} = \hat{i} + 2\hat{j}$.

If vectors $\overrightarrow {A} = \cos\omega t\hat i + \sin\omega t\hat j$ and $\overrightarrow {B} = \cos\frac{\omega t}{2}\hat i + \sin\frac{\omega t}{2}\hat j$ are functions of time,then the value of $t$ at which they are orthogonal to each other is:

Explain the Right-Hand Screw Law.

The diagonals of a parallelogram are $2\,\hat{i}$ and $2\,\hat{j}$. What is the area of the parallelogram in square units?