Final answer:
The statement is false as the curl of a cross product does not simply scale an original vector like the vector x in the identity. Option B is correct.
Step-by-step explanation:
The statement 'the identity curl(v × x) = 2x holds for all vectors v = ai + bj + ck when x = xi + yj + zk' is false. This is because the cross product of two vectors produces a new vector that is orthogonal to the plane containing the two original vectors, and the curl of this resulting vector field does not simplify to a constant vector like 2x.
When we look at the cross product of unit vectors, the rules from vector calculus state that the cross product of two different unit vectors in cyclic order is the third unit vector (i × j = k, j × k = i, k × i = j).
If the order is not cyclic, it results in the negative of the third unit vector (j × i = -k). Any cross product of the same unit vector vanishes (i × i = j × j = k × k = 0). This demonstrates that the curl of a cross product of two vectors is not simply a scaling of one of the original vectors.