Given that $\vec{A} + \vec{B} = \vec{C}$. If $|\vec{A}| = 4, |\vec{B}| = 5$ and $|\vec{C}| = \sqrt{61}$,the angle between $\vec{A}$ and $\vec{B}$ is ....... $^o$

If the magnitude of the sum of two vectors is equal to the magnitude of the difference of the two vectors,the angle between these vectors is ........ $^o$.

If $A$ and $B$ are two non-zero vectors having equal magnitude,the angle between the vectors $A$ and $A - B$ is

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:

The resultant of $\overrightarrow P$ and $\overrightarrow Q$ is perpendicular to $\overrightarrow P$. What is the angle between $\overrightarrow P$ and $\overrightarrow Q$?

Two forces are such that the sum of their magnitudes is $18 \; N$ and their resultant is $12 \; N$,which is perpendicular to the smaller force. Then the magnitudes of the forces are: