ABCD-parallelogram, O-point of intersection of diagonals, M-midpoint of AB, vector DA = vector a, vector DC = vector b.

ABCD-parallelogram, O-point of intersection of diagonals, M-midpoint of AB, vector DA = vector a, vector DC = vector b. Express the following vectors in terms of vectors a and b: a) vector DB b) vector DO c) vector AC d) vector DM

Let us express the vectors needed in the specification, taking into account the rule: the beginning of the desired vector coincides with the beginning of the vector written in the equality with the + sign, and the end of the sought vector coincides with the end of the vector written in the equation with the + sign. DC = a; AB = b.

a) vector DB = vector a + vector b = DA + AB;

b) vector DO = vector DB / 2 = (a + b) / 2.

c) vector AC = vector AD + vector DC = -DA + DC = -a + b, since the vetora DC and AB are equal to b.

d) vector DM = vector DA + 1/2 * vector AB = (a + 1/2 * b).

When solving, the rule was used: parallel vectors are equal.