How Do You Calculate the Position Vector of Point P in a Given Ratio?

[Random-Hero-]

Homework Statement

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)

The Attempt at a Solution

Well I assume it's sort of like finding the midpoint, except I would do something like (-1+4)/1.5 etc.

Am I correct? Do I just divide the sum of the numbers by 3/2 hence the ratio? or am I going about this the wrong way?

 

[Mark44]

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.

It shouldn't be too hard to find that point.
Assuming for the moment that the 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.

 

[Random-Hero-]

Is this a descent answer?

If AP:PB=3:2 then AP:AB=3:(3+2)=3:5
P = A + (B-A)*3/5
P = (-1,6,4)+(5,-5,-5)*3/5
P = (-1,6,4)+(3,-3,-3)
P = (2,3,1)

Am I correct? Can anybody clarify?