Consider the cubic system having a set of crystal panes whose miller indices are (hkl). a) prove reciprocal vector ghkl is normal to the (hkl) plane. b) show that the separation of these planes is 2π times the inverse of the length ghkl.

A12 mm diameter shaft runs in a plain cylindrical bush 30 mm long that is located in an 18 mm diameter hole in a housing. the shaft-inner bush fit is h8 f and the outer bush-housing fit is h7-p6. make a fully cimensioned sketch of the bush with tolerances. find the maximum and minimum clearance or interference for both fits on the inner and outer diameters of the bush