Find the position vector of a point which divides the join of points with position vectors and externally in the ratio 2:1.

Given: two position vectors are

To find: position vector of the point which divided the join of points of given vectors in 2:1 externally

The formula used: The position vector of a point which divides the line of position vectors Y and X in the ratio m:n externally is given by,

Let the required position vector be

Here m = 2, n = 1,

Therefore,

Hence, the required position vector is