The angle between the two vectors $\overrightarrow{A} = 5\hat{i} + 5\hat{j}$ and $\overrightarrow{B} = 5\hat{i} - 5\hat{j}$ will be ....... $^\circ$.

If $\overrightarrow{A}$ and $\overrightarrow{B}$ are two vectors,then which of the following are correct?
$(a) \ (\overrightarrow{A} \times \overrightarrow{B}) \perp \overrightarrow{A}$
$(b) \ (\overrightarrow{A} \times \overrightarrow{B}) \perp \overrightarrow{B}$
$(c) \ (\overrightarrow{A} \times \overrightarrow{B}) \perp (\overrightarrow{A} + \overrightarrow{B})$
$(d) \ (\overrightarrow{A} \times \overrightarrow{B}) \perp (\overrightarrow{A} - \overrightarrow{B})$
$(e) \ (\overrightarrow{A} \times \overrightarrow{B}) \perp (\overrightarrow{A} \cdot \overrightarrow{B})$

Find the angle between the two vectors: $\vec{a}=3 \hat{i}+2 \hat{j}+5 \hat{k}$ and $\vec{b}=5 \hat{i}+3 \hat{j}+\hat{k}$.

The area of the parallelogram formed by vectors $\vec{P} = 2\hat{i} - \hat{j} + 5\hat{k}$ and $\vec{Q} = 3\hat{i} - 2\hat{j} + 4\hat{k}$ is

The area of the parallelogram determined by vectors $A = 2\hat{i} + \hat{j} - 3\hat{k}$ and $B = 12\hat{j} - 2\hat{k}$ is approximately:

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-$II$
$(a) |\vec{A} \times \vec{B}| = 0$	$(i) \theta = 30^{\circ}$
$(b) |\vec{A} \times \vec{B}| = 8$	$(ii) \theta = 45^{\circ}$
$(c) |\vec{A} \times \vec{B}| = 4$	$(iii) \theta = 90^{\circ}$
$(d) |\vec{A} \times \vec{B}| = 4\sqrt{2}$	$(iv) \theta = 0^{\circ}$