If $\vec{A} + \vec{B} = \vec{C}$ and $A + B = C$,what is the angle between $\vec{A}$ and $\vec{B}$?

Given $\vec{A}=(2 \hat{i}-3 \hat{j}+\hat{k})$,$\vec{B}=(3 \hat{i}+\hat{j}-2 \hat{k})$ and $\vec{C}=(3 \hat{i}+2 \hat{j}+\hat{k})$. The value of $(\vec{A}+\vec{B}) \cdot \vec{C}$ will be

If the resultant vector of vectors $\vec{A} = 4\hat{i} + 3\hat{j} + 6\hat{k}$ and $\vec{B} = -\hat{i} + 3\hat{j} - 8\hat{k}$ is parallel to a unit vector,then $\vec{R}$ is:

If the angle between two vectors $A$ and $B$ is $120^{\circ}$,then their resultant $C$ will be:

Two vectors of equal magnitude $5$ units have an angle $60^\circ$ between them. Find the magnitude of $(a)$ the sum of the vectors and $(b)$ the difference of the vectors.

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ have equal magnitudes. If the magnitude of $\overrightarrow{A} + \overrightarrow{B}$ is equal to two times the magnitude of $\overrightarrow{A} - \overrightarrow{B}$,then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ will be .......................