The position vectors of two points are R 1 → and R 2 → . Find the position vector of the middle points of the line joining the two points.

Given the two points A and B with position vectors r 1 → and r 2 → , The point C is the mid-point of the displacement vector AB → . The vector R is the position vector of their midpoint. By applying the law of triangular addition of vectors, in the △ AOC , we have, R → = r 1 → + AC → . and in △ BOC , R → = r → 2 + BC → . Adding the two, we have 2 R = r 1 + r 2 + BC + ( - AC ) = r 1 + r 2 . Hence, the position vector of the midpoint is R → = r 1 → + r 2 → 2 .

The position vectors of two points are R 1 → and R 2 → . Find the position vector of the middle points of the line joining the two points.

Given the two points A and B with position vectors r 1 → and r 2 → , The point C is the mid-point of the displacement vector AB → . The vector R is the position vector of their midpoint. By applying the law of triangular addition of vectors, in the △ AOC , we have, R → = r 1 → + AC → . and in △ BOC , R → = r → 2 + BC → . Adding the two, we have 2 R = r 1 + r 2 + BC + ( - AC ) = r 1 + r 2 . Hence, the position vector of the midpoint is R → = r 1 → + r 2 → 2 .