The position vector of the point which divides the join of points and in the ratio 3 : 1 is

We are given points and .

Let these points be

and .

Also, given in the question that,

A point divides AB in the ratio of 3 : 1.

Let this point be C.

⇒ C divides AB in the ratio = 3 : 1

We need to find the position vector of C.

We know the position vector of a point C dividing the line segment joining the points P and Q, whose position vectors are p and q in the ratio m : n internally is given by,

According to the question, here

m : n = 3 : 1

⇒ m = 3 and n = 1

Also,

And

Substituting these values in the formula above, we get

Thus, position vector of the point is .