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

$\overrightarrow{A}$ 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

The unit vector perpendicular to the two vectors $(2\hat{i} + 3\hat{j} + \hat{k})$ and $(\hat{i} - \hat{j} + 2\hat{k})$ is:

Given $|\vec{A}_1| = 2$,$|\vec{A}_2| = 3$,and $|\vec{A}_1 + \vec{A}_2| = 3$. Find the value of $|(\vec{A}_1 + 2\vec{A}_2) \times (3\vec{A}_1 - 4\vec{A}_2)|$.

The angle between the two vectors $\overrightarrow{A} = 5\hat{i} + 5\hat{j}$ and $\overrightarrow{B} = 5\hat{i} - 5\hat{j}$ will be ....... $^\circ$.

$(\vec{a}-\vec{b}) \times(\vec{a}+\vec{b})$ is equal to :