Two vectors $\vec{A}$ and $\vec{B}$ are at right angles to each other,when

The angle between vectors $(\vec{M} \times \vec{N})$ and $(\vec{N} \times \vec{M})$ is ................ (in $^{\circ}$)

$A$ force $F$ applied on a body is written as $F = (\hat{n} \cdot F) \hat{n} + G$,where $\hat{n}$ is a unit vector. The vector $G$ is equal to

The angle between the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\theta$. The value of the triple product $\overrightarrow{A} \cdot (\overrightarrow{B} \times \overrightarrow{A})$ is

For what value of $x$ will the two vectors $\vec{A} = 2\hat{i} + 2\hat{j} - x\hat{k}$ and $\vec{B} = 2\hat{i} - \hat{j} - 3\hat{k}$ be perpendicular to each other?

Show that the area of the triangle formed by the vectors $\vec{a}$ and $\vec{b}$ is one-half of the magnitude of $\vec{a} \times \vec{b}$.