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For each of the following real space lattices, find a set of fundamental reciprocal lattice vectors and classify the reciprocal
lattice according to Bravais lattice type: (a) simple cubic, (b) body-centered cubic, and (c) face-centered cubic. Show your
derivations.

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please help me with the following and make sure its corrcet 100% , pls and thank you
Given position-space lattice vectors a, b and c, show that the reciprocal lattice vectors (see figure) a* = 2pi b x c / a . (b x c), b* = 2pi c x a/ a . (b x c), c* = 2pi a x b/ a . (b x c) are such that a. a* = 2pi, a.b* = 0
please solve it as soon as possible
QEX. Need help with part B. Need theory and full detailed solution.
Question 3 Consider the simple and close-packed hexagonal direct lattices. (a) Find out the general expression for the structure factor for each lattice type. In this context, what is the significance of a complex structure factor? (b) Without resorting to the structure factor, determine in which structure(s) X-ray Bragg reflections arise from the lattice planes (0001), (0002), and (1010). Justify your answer by the use of the above determined structure factor or otherwise and explain the meaning of the four indices describing the above cited lattice planes.