If |a⃗ - b⃗| = |a⃗ + b⃗| in the given figure, what inference can you draw?

$|\vec{a} - \vec{b}| = |\vec{a} + \vec{b}|$ $\Rightarrow |\vec{a} + \vec{b}|^2 = |\vec{a} - \vec{b}|^2$ $\Rightarrow \vec{a}^2 + 2\vec{a}\cdot\vec{b} + \vec{b}^2 = \vec{a}^2 - 2\vec{a}\cdot\vec{b} + \vec{b}^2$ $\Rightarrow 4\vec{a}\cdot\vec{b} = 0 \Rightarrow \vec{a}\cdot\vec{b} = 0$ $\Rightarrow \vec{a} \perp \vec{b}$ The diagonals of a parallelogram are equal if it is a rectangle.