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

Let $\vec{A} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k}$ and $\vec{B} = 4 \hat{i} + \hat{j} + 2 \hat{k}$,then $|\vec{A} \times \vec{B}|$ is equal to:

Obtain the scalar product of unit vectors in the Cartesian coordinate system.

State and explain the characteristics of the vector product of two vectors.

What is the angle between $\vec{A}$ and $\vec{B}$ if $\vec{A}$ and $\vec{B}$ are the adjacent sides of a parallelogram drawn from a common point and the area of the parallelogram is $\frac{AB}{2}$?

The dot product of unit vectors $\hat{n}_1$ and $\hat{n}_2$ that are parallel to $5 \hat{i}+12 \hat{j}$ and $3 \hat{i}+4 \hat{j}$ respectively is