Three forces acting on a body are shown in the figure. To have the resultant force only along the $y-$ direction, the magnitude of the minimum additional force needed is  ........... $N$

Following forces start acting on a particle at rest at the origin of the co-ordinate system simultaneously${\overrightarrow F _1} = - 4\hat i - 5\hat j + 5\hat k$, ${\overrightarrow F _2} = 5\hat i + 8\hat j + 6\hat k$, ${\overrightarrow F _3} = - 3\hat i + 4\hat j - 7\hat k$ and ${\overrightarrow F _4} = 2\hat i - 3\hat j - 2\hat k$ then the particle will move

Explain resolution of vectors. 

Two vectors of magnitude $3$ & $4$ have resultant which make angle $\alpha$ & $\beta$ respectively with them $\{given\, \alpha + \beta \neq 90^o\}$

Three forces acting on a body are shown in the figure. To have the resultant force only along the $y-$ direction, the magnitude of the minimum additional force needed is.........$N$ 

The projection of a vector $\vec r\, = \,3\hat i\, + \,\hat j\, + \,2\hat k$ on the $xy$ plane has magnitude