Recall that FCC and BCC metals are common and these crystal structures feature different slip systems (slip plane and slip direct on combinations). The purpose of this question is to help you derive the angles relevant to slip in these cubic systems. Although you can find these angles listed in a variety of resources, you are encouraged to solve for them so you can further your understanding of cube geometry and prepare yourself for the exam. In the next lecture, we'll learn that the angles featured in this analysis are common to all cubic systems, but the angles are used n different ways when calculations pertaining to slip for different crystal structures. For now, we can just focus on the fact that we are interested in a cubic structure, so we'll solve this generically here and apply what we learn later. You'll want to remember or record the angles that you establish on this homework. Consider the following cubic unit cell: Note there is a (111) plane shaded and two directions are indicated. One of these line segments is a face-diagonal (on the plane) and the ether is a body diagonal (normal to the plane). Two parallel reference axes (labeled 001) are also included. Use what you know about cubes and a convenient fact about the notation of cubic planes and cubic directions to determine the indicated angles.