Two identical masses, each \(1\text{ }\text{kg}\), having velocity vectors:\(\vec{{\mathrm{V}}_{\mathrm{A}}}={\alpha }_{…

Two identical masses, each \(1\text{ }\text{kg}\), having velocity vectors:\(\vec{{\mathrm{V}}_{\mathrm{A}}}={\alpha }_{1}{\mathrm{t}}^{2}\overset{^}{\mathrm{i}}+{\alpha }_{2}\mathrm{t}\overset{^}{\mathrm{j}}+{\alpha }_{3}\overset{^}{\mathrm{k}},\) \(\vec{{\mathrm{V}}_{\mathrm{B}}}={\alpha }_{1}\overset{^}{\mathrm{i}}+{\alpha }_{2}\overset{^}{\mathrm{j}}+{\alpha }_{3}{\mathrm{t}}^{2}\overset{^}{\mathrm{k}},\)where \({\alpha }_{1}=2,\text{ }{\alpha }_{2}=3n,\text{ }{\alpha }_{3}=4p\), and \(n,p\)are constants.

At \(t=1\text{ }\text{s}\), the velocities of \(A\) and \(B\) are orthogonal to each other and the magnitudes of their velocities are equal: \(\left|\vec{{\mathrm{V}}_{\mathrm{A}}}\right|=\left|\vec{{\mathrm{V}}_{\mathrm{B}}}\right|\).

Find the relative displacement between \(A\) and \(B\) at \(t=1\text{ }\text{s}\), and calculate the angular momentum of \(A\) with respect to \(B\).