Problem 1: Below is a unit cell. List the vectors that map out these points. 6 4 V b X Problem 2: Draw the [110] plane and direction. O y b XProblem 3: Below is a hexagonal unit cell. Determine the indices for the direction listed as the green vector. To start with, define it term of the three vector system (al, a2 and z). Next convert it a hexagonal system. The point should be transformed from [UVW] to [uvtw]. u = (20 - V) v = (2V -U) t = - (utv) W = W Remember this is the general conversion process for translating between cubic and hexagonal systems. [UVw]> [uvtw] U,V and W can be thought of the x, y and z-direction in the cubic system. In Hexagonal, u, v and t are the 3 basal plane vectors (al, a2, a3, they are 60" apart, not 90" apart). Also, w is equivalent to Win the cubic system (z-axis).Problem 4: Determine the Miller Indices for the plane given below. Problem 5: Assume that you have a base-centered lattice (atoms are located at the cube corners and in the Bottom and Top face of the cube). Compute the Structure Factor for this system. Note: you can assume, for this problem, that all three directions (a, b and c) have equal length so that you have a cube. O