If $\vec{A} = 2\hat{i} + 3\hat{j} + 8\hat{k}$ is perpendicular to $\vec{B} = -4\hat{i} + 4\hat{j} + \alpha\hat{k}$,then the value of $\alpha$ is:

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

Two vectors $\vec{P}$ and $\vec{Q}$ are at an angle $\theta$ to each other. Which of the following is a unit vector perpendicular to both $\vec{P}$ and $\vec{Q}$?

Which of the following is the unit vector perpendicular to $\vec{A}$ and $\vec{B}$?

If a vector $A=2i+2j+3k$ and $B=3i+6j+nk$ are perpendicular to each other,then the value of $n$ is

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 $^{\circ}$)