Q$\mathrm{.}1.$ The figure below shows a diffraction pattern of FCC Nd$2$Hf$2$O$7$ single$-$crystals. $\{111\}$ family of crystallographic planes are labeled on the patterns. The lengths of R$1,$ R$2$ and R$3$ are measured to be $12\mathrm{.}50,14\mathrm{.}43$ and $20\mathrm{.}41$ mm $,$ respectively. Determine the crystallographic planes represented by dot a and b$.[30$ points$]$