ABCD-parallelogram, АС intersects ВD = О, point М belongs to АD so that АМ refers to this МD

ABCD-parallelogram, АС intersects ВD = О, point М belongs to АD so that АМ refers to this МD = 1 refers to 2. Express the vector ОМ through the vector а = vector ВС, vector в = vector DA

We construct the НК vector through the point O and parallel to BA, which is equal to the vector BA = a and coincides in direction.

Point O divides the diagonals in half, and also halves the НC vector.

Then the vector НК = BA / 2 = b / 2.

Let’s construct a CM vector, the length of which will be equal to the sixth part of AD

Vector DA is equal to BC and opposite in direction, then DA = -BC = -a.

Then the vector MK = -a / 6.

Vector ОМ = OK + КМ = (b / 2) – (a / 6).

Answer: Vector OM is (b / 2) – (a / 6).