If $\vec{P}+\vec{Q}=\vec{P}-\vec{Q}$,then

$A$ force ${F_1} = 1\,N$ acts along the direction of $x = 0$,and a force ${F_2} = 2\,N$ acts along the direction of $y = 0$. Find the resultant force.

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 $\frac{|A_1|}{|A_2|}$.

If the sum of two unit vectors is a unit vector,find the magnitude of their difference.

Two forces $P + Q$ and $P - Q$ make an angle $2 \alpha$ with each other,and their resultant makes an angle $\theta$ with the bisector of the angle between them. Then:

Given that $P + Q + R = 0$. Which of the following statements is true?