The angle between two forces of equal magnitude $R$,if the magnitude of their resultant is $\frac{R}{2}$,is:

Two vectors of the same magnitude have a resultant equal to either of the two vectors. The angle between the two vectors is: (in $^{\circ}$)

What is the angle between $\overrightarrow P$ and the resultant of $(\overrightarrow P + \overrightarrow Q)$ and $(\overrightarrow P - \overrightarrow Q)$?

Given below in Column $-I$ are the relations between vectors $\vec a$,$\vec b$,and $\vec c$,and in Column $-II$ are the orientations of $\vec a$,$\vec b$,and $\vec c$ in the $XY-$ plane. Match the relation in Column $-I$ to the correct orientations in Column $-II$.

Column $-I$	Column $-II$
$(a) \vec a + \vec b = \vec c$	$(i)$ Vector $\vec a$ is along $+Y$,$\vec c$ is along $+X$,and $\vec b$ connects the origin to the tip of $\vec c$
$(b) \vec a - \vec c = \vec b$	$(ii)$ Vector $\vec a$ is along $+X$,$\vec b$ is along $+Y$,and $\vec c$ connects the origin to the tip of $\vec b$
$(c) \vec b - \vec a = \vec c$	$(iii)$ Vector $\vec c$ is along $+X$,$\vec a$ is along $+Y$,and $\vec b$ connects the tip of $\vec c$ to the tip of $\vec a$
$(d) \vec a + \vec b + \vec c = 0$	$(iv)$ Vector $\vec a$ is along $-X$,$\vec b$ is along $-Y$,and $\vec c$ connects the origin to the tip of $\vec b$

The resultant of two forces acting at an angle of $120^{\circ}$ is $10 \,kg$-wt and is perpendicular to one of the forces. That force is

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$. What is the angle between $\vec{A}$ and $\vec{B}$?