a) Define the reciprocal lattice vectors b1, b2, and b3 in terms of unit cellvectors a1, a2, and a3.b) If the primitive unit cell vectors are |a1|=a, |a2|=b, and |a3|=c, calculate thereciprocal lattice constants [b1], [b2], and |b3|.c) Consider a crystal with a primitive unit cell having dimensions a=2Å,b=3Å, and c=4Å. Calculate the lengths of the reciprocal lattice vectors |b1|,[b2], and |b3|.

“Since you have posted multiple questions, we will provide the solution only to the first question…

a) Define the reciprocal lattice vectors b1, b2, and b³ in terms of unit cell vectors a1, a2, and a3. b) If the primitive unit cell vectors are |a1|=a, |a2|=b, and |a3|=c, calculate the reciprocal lattice constants |bi|, [b2], and |b3|. c) Consider a crystal with a primitive unit cell having dimensions a=2Å, b=3Å, and c=4Å. Calculate the lengths of the reciprocal lattice vectors |b1|, [b2], and |b3|.

a) Define the reciprocal lattice vectors b1, b2, and b³ in terms of unit cell vectors a1, a2, and a3. b) If the primitive unit cell vectors are |a1|=a, |a2|=b, and |a3|=c, calculate the reciprocal lattice constants |bi|, [b2], and |b3|. c) Consider a crystal with a primitive unit cell having dimensions a=2Å, b=3Å, and c=4Å. Calculate the lengths of the reciprocal lattice vectors |b1|, [b2], and |b3|.