If the relationship between three vectors is $\vec{A} \cdot \vec{B} = 0$ and $\vec{A} \cdot \vec{C} = 0$,then $\vec{A}$ is parallel to:

Vector $\vec{F_1}$ is in the direction of the positive $X$-axis. If its cross product with another vector $\vec{F_2}$ is zero,what could be the vector $\vec{F_2}$?

For three vectors $\vec{A} = (-x \hat{i} - 6 \hat{j} - 2 \hat{k})$,$\vec{B} = (-\hat{i} + 4 \hat{j} + 3 \hat{k})$ and $\vec{C} = (-8 \hat{i} - \hat{j} + 3 \hat{k})$,if $\vec{A} \cdot (\vec{B} \times \vec{C}) = 0$,then the value of $x$ is:

If $\overrightarrow A = 3\hat i + \hat j + 2\hat k$ and $\overrightarrow B = 2\hat i - 2\hat j + 4\hat k$,then find $|\overrightarrow A \times \overrightarrow B |$.

$A$ vector perpendicular to the vector $(4 \hat{i}-3 \hat{j})$ is

If the vector $2\hat{i} + 3\hat{j} + 8\hat{k}$ is perpendicular to the vector $4\hat{j} - 4\hat{i} + \alpha\hat{k}$,then what is the value of $\alpha$?