(Solved): 13. The right drawing shows the unit cell of copper crystalline structure with lattice constant a. ...

13. The right drawing shows the unit cell of copper crystalline structure with lattice constant a. Calculate the inter-atomic distance between atoms of \( A \) and \( \mathrm{B}, \mathrm{B} \) and \( \mathrm{C} \), and \( \mathrm{A} \) and \( \mathrm{C} \) in a unit of lattice constant a. Use the atomic coordinate and vector approach. Show me three steps for each calculation.