For the resultant of the two vectors to be maximum, what must be the angle between them....... $^o$

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

Two vectors $\vec A$ and $\vec B$ have equal magnitudes. The magnitude of $(\vec A + \vec B)$ is $‘n’$ times the magnitude of $(\vec A - \vec B)$. The angle between $ \vec A$ and $\vec B$ is

Two forces $3\,N$ and $2\, N$ are at an angle $\theta$ such that the resultant is $R$. The first force is now increased to $ 6\,N$ and the resultant become $2R$. The value of is ....... $^o$

Two forces acting on point $A$ along their side and having magnitude reciprocal to length of side then resultant of these forces will be proportional to

$\vec{A}$ is a vector of magnitude $2.7$ units due east. What is the magnitude and direction of vector $4 \vec{A}$ ?