Given the point A (1,2)and AB (3/2) ,BC =(-1/2) and CD = (_2/_2). Find the position vector OB ,OC and OD , where 0 is the origin (0,0)?

To find the position vectors OB, OC, and OD, we need to add the vectors AB, BC, and CD to the position vector of point A.

Given:
A(1,2)
AB = (3/2)
BC = (-1/2)
CD = (-2/2)

Position vector of A:
OA = (1,2)

Position vector of B:
OB = OA + AB
OB = (1,2) + (3/2)
OB = (1 + 3/2, 2 + 0)
OB = (5/2, 2)

Position vector of C:
OC = OB + BC
OC = (5/2, 2) + (-1/2)
OC = (5/2 - 1/2, 2 - 1/2)
OC = (4/2, 3/2)
OC = (2, 3/2)

Position vector of D:
OD = OC + CD
OD = (2, 3/2) + (-2/2)
OD = (2 - 2/2, 3/2 - 2/2)
OD = (2 - 1, 1/2)
OD = (1, 1/2)

Therefore, the position vectors are:
OB = (5/2, 2)
OC = (2, 3/2)
OD = (1, 1/2)