position vector given points, but ratio between the two points?

**Use vectors to find the position vector of point 'P' if 'P' divides AB in the ratio 3:2 given A(-1,6,4) and B(4,1,-1).**

This is what I'm thinking so far..

Point P is 3/5 the way along from A to B. When you divide something in the ratio 3:2, one part will be 3/5 of the total and the other will be 2/5 of the total.

coordinates of P are (x, y, z), the position vector of point P will be the vector (x - (-1), y - 6, z - 4). This vector has the same direction as AP and the same magnitude.

Am I on the right track here fellas?