In nature, substances often possess a crystalline structure. The basic component

Question

In nature, substances often possess a crystalline structure. The basic component of a crystal is the unit cell, such as the rectangular parallelpiped illustrated in the figure (Figure 1) . (For the purposes of this problem, take L_1, L_2, and L_3 to be positive.) Find the following quantities. When the question asks for a vector, express your answer as an ordered triplet. That is, a vector with length a in the x direction, length b in the y direction, and length c in the z direction should be written as (a,b,c).

Explanation / Answer

Answered By Mohsen

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a)   V1 = (L2, 0, L3)

b) V2 = (L2, L1, L3)

c)   V3 = (0, L1, 0)

d) 2 V3 + 3 V2 = (3 L2, 5 L1, 3 L3)

d) |V1| = (L2^2 + L3^2)

e) |V2| = (L2^2 + L1^2+ L3^2)

f) |V3| = L1

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