For AC/CB to be 2, C has to be placed at 2/3 of the line segment AB. The parametric equation for the line passing through AB is:

where t is the parameter. This gives the equation:

At t=0, we get A and at t=1, we get B. Therefore, by setting t=2/3, we'll get our point C:

C=(4,-1,2)+(2/3)(-3,6,1)

Then, AC is given by:

AC=C-A=(4,-1,2)+(2/3)(-3,6,1)-(4,-1,2)=(2/3)(-3,6,1)

AC=(-2,4,2/3)