Two forces with equal magnitudes $F$ act on a body and the magnitude of the resultant force is $F/3$. The angle between the two forces is

Two vectors $\vec{A}$ and $\vec{B}$ have equal magnitudes. Then the vector $\vec{A} + \vec{B}$ is perpendicular to:

When are the magnitudes of $\vec{A} + \vec{B}$ and $\vec{A} - \vec{B}$ equal?

Two vectors $\vec A$ and $\vec B$ have magnitudes $2$ and $1$ respectively. If the angle between $\vec A$ and $\vec B$ is $60^{\circ}$,then which of the following vectors may be equal to $\frac{\vec A}{2} - \vec B$?

With respect to a rectangular cartesian coordinate system,three vectors are expressed as $\vec a = 4\hat i - \hat j$,$\vec b = -3\hat i + 2\hat j$,and $\vec c = -\hat k$,where $\hat i, \hat j, \hat k$ are unit vectors along the $X, Y,$ and $Z$-axis respectively. The unit vector $\hat r$ along the direction of the sum of these vectors is:

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 $^{\circ}$)