What is the angle between $\vec{A}$ and $\vec{B}$ if $\vec{A}$ and $\vec{B}$ are the adjacent sides of a parallelogram drawn from a common point and the area of the parallelogram is $\frac{AB}{2}$?

The two vectors have magnitudes $3$ and $5$. If the angle between them is $60^o$,then the dot product of the two vectors will be:

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 $^{\circ}$)

Two forces $\vec F_1 = 5\hat i + 10\hat j - 20\hat k$ and $\vec F_2 = 10\hat i - 5\hat j - 15\hat k$ act on a single point. The angle between $\vec F_1$ and $\vec F_2$ is nearly . . . . . . $^\circ$.

$\vec{A}$ is a vector quantity such that $|\vec{A}| =$ nonzero constant. Which of the following expressions is true for $\vec{A}$?

The angle between vectors $(\overrightarrow {A} \times \overrightarrow {B})$ and $(\overrightarrow {B} \times \overrightarrow {A})$ is