1. In an experiment, three forces are acting on a particle.  ${F}_{1}=(7i−j)$ newtons and ${F}_{2}=(xi+yj)$ newtons are both constant forces, although the values of x and y are initially unknown.  The third force is${F}_{3}=(ki+k\sqrt{}3j)$ newtons, where $k\geq0$ is a parameter that can be varied by the experimenters.  The resultant force R acting on the particle is given by $R={F}_{1}+{F}_{2}+{F}_{3}.$

Given that R = 0 when the magnitude of F₃ is 10 newtons, find the exact values of x and y.