1. In an experiment, three forces are acting on a particle.  ${F}_{1}=7i-j$newtons and ${\text{F}}_{2}=xi+yj$ newtons are both constant forces, although the values of x and y are initially unknown.  The third force is${F}_{3}=ki+k\sqrt{3}j$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 ${F}_{3}$ is 10 newtons, find the exact values of x and y.