The points A and B have coordinates (2,4,1) and (3,2,-1) respectively. The point C is such that OC = 2OB, where O is the origin. Find the distance between A and C.

To find the distance between the points A and C, we want to find the magnitude of the vector AC. In order to do this, we must first find the vector AC, which we do by using their position vectors. We are given that the position vector of A is (2,4,1), and the position vector of C in terms of OB. So first, we calculate OC:

OC = 2OB = 2*(3,2,-1) = (6,4,-2)

Now we have OA and OC, we can find the vector AC by subtracting OA from OC:

AC = OC - OA = (6,4,-2) - (2,4,1) = (4,0,-3)

Now it's just a case of finding the magnitude of this vector AC, which will give us the distance between the points A and C.

| AC | = (4^2 + 0^2 + 3^2) ^ (1/2) = 25^(1/2) = 5