Physics - Vectors Question with Solution | TestHub

Two vectors are perpendicular if their dot product is zero.

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

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

Since $\vec{A}\cdot \vec{B}=\vec{B}\cdot \vec{A}$, the equation simplifies to:

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

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

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