$A$ vector perpendicular to the vector $(4 \hat{i}-3 \hat{j})$ is

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

Explain the geometrical interpretation of the scalar product of two vectors.

For two vectors $\vec{P}$ and $\vec{Q}$, $\vec{P} \cdot \vec{Q} = |\vec{P} \times \vec{Q}|$. The magnitude of $\vec{R} = \vec{P} + \vec{Q}$ is:

If $\vec A = 2\hat i + \hat j - \hat k$,$\vec B = \hat i + 2\hat j + 3\hat k$ and $\vec C = 6\hat i - 2\hat j - 6\hat k$,then the angle between $(\vec A + \vec B)$ and $\vec C$ will be ....... $^o$.

Show that $\vec{a} \cdot(\vec{b} \times \vec{c})$ is equal in magnitude to the volume of the parallelepiped formed by the three vectors $\vec{a}, \vec{b}$ and $\vec{c}$.