If a and b represents the diagonals of a square, then

The correct answer is Option (3) → \(\vec{a}\cdot\vec{b}=0\)

The diagonals of a square are perpendicular, so the angle between \(\vec{a}\) and \(\vec{b}\) is \(90^\circ\):

    \(\vec{a}\cdot\vec{b} = |\vec{a}|\,|\vec{b}|\cos90^\circ = 0\)

This can also be checked with the sides. If the sides from one corner are \(\vec{p}\) and \(\vec{q}\), with \(|\vec{p}| = |\vec{q}|\) and \(\vec{p}\cdot\vec{q} = 0\), the diagonals are \(\vec{p}+\vec{q}\) and \(\vec{q}-\vec{p}\):

    \((\vec{p}+\vec{q})\cdot(\vec{q}-\vec{p}) = |\vec{q}|^2 - |\vec{p}|^2 = 0\)