1. The problem statement, all variables and given/known data For a cubic crystal lattice: The intercepts of a plane are -1, 1, and 2 along the x, y, and z axes, respectively. The Miller index is (!2 2 1). Find the direction vector normal to the plane. 2. Relevant equations 3. The attempt at a solution In my book it states that a cubic lattice will have the same value for the direction vector if the crystal is cubic. "a plane and the direction normal to the plane have precisely the same indices" I would then be lead to believe that the direction normal should be [ !2 2 1] However, according to the book, "The direction vector has projections of 2a, a, and 0 along the x, y, and z coordinate axes, respectively. The Miller indices for the direction are then . This is an example problem but it makes no sense to me. Can anyone clear up this discrepancy? It seems to me like this may be a typo, but I don't have enough knowledge to say one way or the other.