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

If $|\vec{A} + \vec{B}| = |\vec{A}| = |\vec{B}|$,then the angle between $\vec{A}$ and $\vec{B}$ is ............ $^o$.

Magnitudes of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are $4$ units and $3$ units respectively. If these vectors are $(i)$ in the same direction $(\theta = 0^{\circ})$ and $(ii)$ in the opposite direction $(\theta = 180^{\circ})$,find the magnitude of the resultant vector in each case.

$A$ unit vector in the direction of the resultant vector of $\vec{A} = -2 \hat{i} + 3 \hat{j} + \hat{k}$ and $\vec{B} = \hat{i} + 2 \hat{j} - 4 \hat{k}$ is

Find the magnitude and direction of the resultant of two vectors $A$ and $B$ in terms of their magnitudes and the angle $\theta$ between them.

The resultant of two forces $3P$ and $2P$ is $R$. If the first force is doubled,then the resultant is also doubled. The angle between the two forces is ........... $^o$.