If $\vec{P}+\vec{Q}=\vec{0}$,then which of the following is necessarily true?

The vector sum of two forces is perpendicular to their vector difference. In this case,the forces:

The magnitudes of vectors $\overrightarrow{A}$,$\overrightarrow{B}$,and $\overrightarrow{C}$ are $12$,$5$,and $13$ units respectively,and $\overrightarrow{A} + \overrightarrow{B} = \overrightarrow{C}$. Then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

The angle $\beta$ between vector $\overrightarrow{A}$ and the resultant vector $(\overrightarrow{A}-\overrightarrow{B})$ is given by:

If $|\vec{A} + \vec{B}| = |\vec{A}| = |\vec{B}|$,then the angle between $\vec{A}$ and $\vec{B}$ is ............ $^o$.

Give the equations to find the magnitude and direction of the resultant vector of two vectors $\vec{A}$ and $\vec{B}$ that are inclined at an angle $\theta$ to each other.