Physics - Vectors Question with Solution | TestHub

Given that the vector sum is perpendicular to the vector difference.

$(\vec{A}+\vec{B})\cdot (\vec{A}-\vec{B})=0$

$\vec{A}\cdot \vec{A}-\vec{A}\cdot \vec{B}+\vec{B}\cdot \vec{A}-\vec{B}\cdot \vec{B}=0$

Since $\vec{A}\cdot \vec{B}=\vec{B}\cdot \vec{A}$, we get:

$|\vec{A}{|}^2-|\vec{B}{|}^2=0$

$|\vec{A}|=|\vec{B}|$

Thus, the forces $\vec{A}$ and $\vec{B}$ are equal in magnitude.

Answer: equal in magnitude