What is the minimum number of vectors of equal magnitude required to produce a zero resultant vector?

The vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$. The angle between the two vectors is: (in $^{\circ}$)

Which vector must be added to the resultant vector $\vec{P} = 2\hat{i} + 7\hat{j} - 10\hat{k}$ and $\vec{Q} = \hat{i} + 2\hat{j} + 3\hat{k}$ to obtain a unit vector along the $X$-axis?

Two forces are such that the sum of their magnitudes is $18 \,N$ and their resultant is perpendicular to the smaller force and the magnitude of the resultant is $12 \,N$. Then the magnitudes of the forces are:

If the square of the resultant of two forces of equal magnitude is equal to three times their product,then the angle between them is ........ $^o$.

$A$ force of $6\,N$ and another of $8\,N$ can be applied together to produce the effect of a single force of $..........\,N$