If $a + b + c = 0$,then $a \times b$ is equal to:

The area of the parallelogram represented by the vectors $\overrightarrow A = 2\hat i + 3\hat j$ and $\overrightarrow B = \hat i + 4\hat j$ is ....... $units^2$.

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 $\overrightarrow{A} = a_{1} \hat{\imath} + a_{2} \hat{\jmath}$ and $\overrightarrow{B} = b_{1} \hat{\imath} + b_{2} \hat{\jmath}$ are perpendicular to each other,then:

$\vec{A}$,$\vec{B}$,and $\vec{C}$ are three non-collinear,non-coplanar vectors. What can you say about the direction of $\vec{A} \times (\vec{B} \times \vec{C})$?

$A$ 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: