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

To find the position vectors OB, OC, and OD, we need to add the coordinates of the given points to the coordinates of the origin.

Given:
A (1,2)
B (1+3, 2+2) = (4,4)
C (4-1, 4+2) = (3,6)
D (3-2, 6-2) = (1,4)

Now, we can find the position vectors:
OB = B - O = (4,4) - (0,0) = (4,4)
OC = C - O = (3,6) - (0,0) = (3,6)
OD = D - O = (1,4) - (0,0) = (1,4)

Therefore, the position vectors are:
OB = (4,4)
OC = (3,6)
OD = (1,4)