Turquoise is an attractive bluish gemstone often fashioned into jewelry by Native Americans. In one XRD experiment, a turquoise sample was shown to have a triclinic Bravais lattice. In a Cartesian frame the measured basis vectors are

where basis vector a is taken to lie along the \(x\)-axis and lengths are in \(\mathrm{nm}\).

(a) What is the angle between basis vectors \(\mathbf{b}\) and \(\mathbf{c}\) ?

(b) What is the volume of the triclinic Bravais lattice?

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a = 0.741 b= 0.3221+0.692 0.344+0.241+0.896k,