Awave on a small lake has an amplitude of 0.1. what happens to the energy of the wave by doubling its height to 0.2 meters

As we know that energy of wave depends on amplitude as per following relation

here we know that

k = constant

A = amplitude of wave

here we know that amplitude is doubled

so here as per above formula the energy of wave will increase by 4 times

as we know that

so energy is 4 times of initial value

no. dot product   =0 when vecs at right angles