Forces $F_1$ and $F_2$ act on a point mass in two mutually perpendicular directions. The resultant force on the point mass will be

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

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 $r_1=2 \hat{x}$ and $r_2=2 \hat{y}$, where $\hat{x}$ and $\hat{y}$ are unit vectors along the $X$-axis and $Y$-axis respectively, then the magnitude of $r_1+r_2$ is

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 sum of the magnitudes of two vectors acting at a point is $18$ and the magnitude of their resultant is $12$. If the resultant is at $90^{\circ}$ with the vector of smaller magnitude,then the magnitudes of the vectors are