If a vector  $\overrightarrow{P}$ making angles $\alpha ,\beta$  and $\gamma$ respectively with the X, Y and Z axes respectively. Then  ${\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma =a$. If the resultant of n vectors of different magnitudes acting at a point is zero, then the minimum value of n is b. then  $(a^2+b^2)$

 $$\begin{gathered} {\sin }^2\alpha +{\sin }^2\beta +\sin \gamma =1-c{s}^2\alpha +1-{\cos }^2\beta +1-{\cos }^2\gamma \\ =3-({\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma )=3-1=2 \end{gathered}$$
 If vectors are of equa magnitude then two vectors can give zero resultant, if they works in  opposite direction. But if the vectors are of different magnitudes then minimum three  vectors are required to give zero resultant.