Two non-zero vectors $\vec{A}$ and $\vec{B}$ are such that $(\vec{A}+\vec{B}) \cdot (\vec{A}-\vec{B}

Question

Two non-zero vectors $\vec{A}$ and $\vec{B}$ are such that $(\vec{A}+\vec{B}) \cdot (\vec{A}-\vec{B}) = 0$. The correct relation between the two vectors is

Professor PC Thomas Classes · Answer

(a) : $(\vec{A}+\vec{B}) \cdot (\vec{A}-\vec{B}) = \vec{A}\cdot\vec{A} - \vec{A}\cdot\vec{B} + \vec{B}\cdot\vec{A} - \vec{B}\cdot\vec{B} = |\vec{A}|^2 - |\vec{B}|^2$. \ Since the dot product is zero, $|\vec{A}|^2 - |\vec{B}|^2 = 0 \implies |\vec{A}| = |\vec{B}|$.