If diagonals of a parallelogram are $(5\hat i - 4\hat j + 3\hat k)$ and $(3\hat i + 2\hat j - \hat k)$,then its area is

If $|\overrightarrow A \times \overrightarrow B | = |\overrightarrow A \cdot \overrightarrow B |$,then the angle between $\overrightarrow A$ and $\overrightarrow B$ will be ........ $^o$.

The diagonals of a parallelogram are represented by vectors $\vec{A} = 5\hat{i} - 4\hat{j} + 3\hat{k}$ and $\vec{B} = 3\hat{i} - 2\hat{j} - \hat{k}$. What is the area of the parallelogram (in $\sqrt{3}$)?

If $\overrightarrow{P} \cdot \overrightarrow{Q} = PQ,$ then the angle between $\overrightarrow{P}$ and $\overrightarrow{Q}$ is ....... $^\circ$.

If $\overrightarrow{ P } \times \overrightarrow{ Q } = \overrightarrow{ Q } \times \overrightarrow{ P }$,the angle between $\overrightarrow{ P }$ and $\overrightarrow{ Q }$ is $\theta$ $(0^{\circ} < \theta < 360^{\circ})$. The value of $\theta$ will be ........ (in $^{\circ}$)

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