Determine a set of (non-orthogonal) base vectors a = j + k, b = i + k, and c = i + j.
(a) Establish their reciprocal vectors and hence express the vectors p = 3i - 2j + k, q = i + 4j, and r = -2i + j + k in terms of the base vectors a, b, and c.
(b) Verify that the scalar product p * q has the same value, -5, when evaluated using either set of components.