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

$\overrightarrow{A}$ and $\overrightarrow{B}$ are two vectors given by $\overrightarrow{A} = 2\widehat{i} + 3\widehat{j}$ and $\overrightarrow{B} = \widehat{i} + \widehat{j}$. The magnitude of the component (projection) of $\overrightarrow{A}$ on $\overrightarrow{B}$ is

If $\overrightarrow{A} = 2\widehat{i} - 2\widehat{j}$ and $\overrightarrow{B} = 2\widehat{k}$,then find the dot product $\overrightarrow{A} \cdot \overrightarrow{B}$.

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 the vector $(\hat{a} + 2\hat{b})$ is perpendicular to the vector $(5\hat{a} - 4\hat{b})$,then the angle between $\hat{a}$ and $\hat{b}$ is ........ $^\circ$.

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