If the magnitudes of vectors $\vec P$,$\vec Q$,and $\vec R$ are $5$,$12$,and $13$ units respectively,and if $\vec P + \vec Q = \vec R$,then the angle between $\vec Q$ and $\vec R$ is:

If the magnitude of the sum of two vectors is equal to the magnitude of the difference of two vectors,then the angle between them is: (in $^{\circ}$)

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is . . . . . . (in $^{\circ}$)

Two vectors $\vec A$ and $\vec B$ have equal magnitudes. The magnitude of $(\vec A + \vec B)$ is $n$ times the magnitude of $(\vec A - \vec B)$. The angle between $\vec A$ and $\vec B$ is

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 .......................

The sum of the magnitudes of two forces is $25 \,N$. The resultant of these forces is perpendicular to the smaller force and has a magnitude of $10 \,N$. The two forces are: