If for two vectors $\vec{A}$ and $\vec{B}$,$\vec{A} \times \vec{B} = 0$,then the vectors:

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 $\frac{AB}{2}$?

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

Write the necessary condition for the scalar product of two mutually perpendicular vectors.

Two position vectors are given by $\overrightarrow{r_1} = (1, 1, 1)$ and $\overrightarrow{r_2} = (1, -1, 1)$. Find the unit vector in the direction of $\overrightarrow{r_1} \times \overrightarrow{r_2}$.

If $\vec{a}$ and $\vec{b}$ make an angle $\cos^{-1}\left(\frac{5}{9}\right)$ with each other,then $|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|$ for $|\vec{a}|=n|\vec{b}|$. The integer value of $n$ is . . . . . . .