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

Which of the following is the unit vector perpendicular to $\vec{A}$ and $\vec{B}$?

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

Define the scalar product and obtain the magnitude of a vector from it. Mention the direction of scalar product.

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

If $\vec{P} = b \hat{i} + 6 \hat{j} + \hat{k}$ and $\vec{Q} = \hat{i} - a \hat{j} + 4 \hat{k}$ are perpendicular to each other,and $3b - a = 5$,find the values of $a$ and $b$.