ABCD is a parallelogram, O is the point of intersection of the diagonals AC and BD, K is the midpoint

ABCD is a parallelogram, O is the point of intersection of the diagonals AC and BD, K is the midpoint of the cut AO, it is given that AB = vector a and AD = vector b. Express vectors a and b vector AO and DK.

Obviously, the vector AC = AD + AB = b + c. Since in the parallelogram the diagonals at the intersection point are divided in half, we get:

AO = 1/2 AC = 1/2 * (b + c).

| AK | = 1/2 | AO | by the condition of the problem, then:

AK = 1/2 AO = 1/2 * 1/2 * (b + c) = 1/4 * (b + c).

The vector DK is equal to the difference:

AD – AK = b – 1/4 * (b + c) = 3/4 * b – 1/4 * c.