If $\vec{A} + \vec{B} + \vec{C} = 0$,then $\vec{A} \times \vec{B}$ is equal to:

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 $\overrightarrow {A} = 2\hat i + 3\hat j - \hat k$ and $\overrightarrow {B} = - \hat i + 3\hat j + 4\hat k$,a unit vector perpendicular to both $\overrightarrow {A}$ and $\overrightarrow {B}$ will be

Consider three vectors $A = \hat{i} + \hat{j} - 2\hat{k}$,$B = \hat{i} - \hat{j} + \hat{k}$,and $C = 2\hat{i} - 3\hat{j} + 4\hat{k}$. $A$ vector $X$ of the form $X = \alpha A + \beta B$ (where $\alpha$ and $\beta$ are scalars) is perpendicular to $C$. The ratio of $\alpha$ to $\beta$ is: (in $: 1$)

Define the scalar product of two vectors.

$A$ vector $\overrightarrow{F}_1$ is along the positive $X$-axis. If its vector product with another vector $\overrightarrow{F}_2$ is zero,then $\overrightarrow{F}_2$ could be: