Question

If vector u, vector v, vector w are non-coplanar vectors and p, q are real numbers, then the equality [ 3vector u, p vector v, p vector w] − [ pv w qu ] − [ 2vector w, q vector v,  q vector u ] = holds for
(a) exactly two values of ( p, q)
(b) more than two but not all values of ( p , q)
(c) all values of ( p, q)
(d) exactly one value of ( p, q)

Answer 1

As a quadratic in p, roots are real

Thus (p, q) ≡ (0, 0) is the only possibility.​