ABCD – parallelogram, O – intersection point of diagonals, M – midpoint of AC, AB = a, AD = b.

ABCD – parallelogram, O – intersection point of diagonals, M – midpoint of AC, AB = a, AD = b. Express the following vectors in terms of vectors a and b: 1) AC; 2) AO; 3) BD; 4) AM; 5) DM.

The parallelogram property says: at the point of intersection, the diagonals are halved. Hence the points O and M coincide.

1) AC = AB + AD = a + b;

2) AO = 1/2 * AC = 1/2 (a + b);

3) BD = AB – AD = a – b;

4) AM = AO = 1/2 (a + b);

5) DM = 1/2 * DB = 1/2 (a – b).