Which of the following forces cannot be a resultant of $5\, N$ and $7\, N$ forces (in $, N$)?

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 forces of magnitudes $3 \, N$ and $4 \, N$ are acting on an object. If the angle between them is $90^\circ$,then their resultant force is ... $N$.

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 $^{\circ}$)?

What is the minimum number of coplanar vectors having different magnitudes that can be added to give a zero resultant?

If $\sqrt{A^2+B^2}$ represents the magnitude of the resultant of two vectors $(\vec{A}+\vec{B})$ and $(\vec{A}-\vec{B})$,then the angle between the two vectors $\vec{A}$ and $\vec{B}$ is