For the reaction $2A\stackrel{ }{\to }B+3C$;if $-\frac{d\left[A\right]}{dt}=k_1{\left[A\right]}^2;\frac{d\left[B\right]}{dt}=k_2{\left[A\right]}^2;\frac{d\left[C\right]}{dt}=k_3{\left[A\right]}^2$. The correct relation between $k_1,k_2$ and $k_3$ is :