3d Geometry

A line passes through \(A(4,-6,-2)\) and \(B(16,-2,4)\). The point \(P(a, b, c)\), where \(a, b, c\) are non-negative integers, on the line \(A B\) lies at a distance of 21 units, from the point \(A\). The distance between the points \(P(a, b, c)\) and \(Q(4,-12,3)\) is equal to __________.