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

What is the value of $(\vec{A} + \vec{B}) \cdot (\vec{A} \times \vec{B})$?

The modulus of the vector product of two vectors is $\frac{1}{\sqrt{3}}$ times their scalar product. The angle between the vectors is

Why is the product of two vectors not commutative?

If $|\vec A| = 2$ and $|\vec B| = 4$,then match the relation in Column $-I$ with the angle $\theta$ between $\vec A$ and $\vec B$ in Column $-II$.

Column $-I$	Column $-II$
$(a) \vec A \cdot \vec B = 0$	$(i) \theta = 0^\circ$
$(b) \vec A \cdot \vec B = +8$	$(ii) \theta = 90^\circ$
$(c) \vec A \cdot \vec B = 4$	$(iii) \theta = 180^\circ$
$(d) \vec A \cdot \vec B = -8$	$(iv) \theta = 60^\circ$

If $\overrightarrow{F}=(4 \hat{i}-10 \hat{j}) \text{ N}$ and $\overrightarrow{r}=(-5 \hat{i}-3 \hat{j}) \text{ m}$,then $(\overrightarrow{r} \times \overrightarrow{F})$ is