What displacement must be added to the displacement $25\hat i - 6\hat j\,\,m$ to give a displacement of $7.0\, m$ pointing in the $X- $direction

Figure shows a body of mass m moving with a uniform speed $v$ along a circle of radius $r$. The change in velocity in going from $A$ to $B$ is

The sum of three forces ${\vec F_1} = 100\,N,{\vec F_2} = 80\,N$ and ${\vec F_3} = 60\,N$ acting on a particle is zero. The angle between $\vec F_1$ and $\vec F_2$ is nearly .......... $^o$

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

Two forces of $10 \,N$ and $6 \,N$ act upon a body. The direction of the forces are unknown. The resultant force on the body may be .........$N$

Explain the analytical method for vector addition.