What should be the angle $\theta$ between two vectors $\vec{A}$ and $\vec{B}$ so that the magnitude of the resultant vector is minimum (in $^{\circ}$)?

Given that $A_1+A_2=5 A_3$ and $A_1-A_2=3 A_3$, where $A_3=2 \hat{i}+4 \hat{j}$, find the value of $\frac{|A_1|}{|A_2|}$.

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

At what angle do two forces $(x + y)$ and $(x - y)$ act so that their resultant is $\sqrt{x^2 + y^2}$?

The magnitudes of vectors $\overrightarrow{A}$,$\overrightarrow{B}$,and $\overrightarrow{C}$ are $12$,$5$,and $13$ units respectively,and $\overrightarrow{A} + \overrightarrow{B} = \overrightarrow{C}$. Then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

The resultant force of $5 \, N$ and $10 \, N$ cannot be ........ $N$.