Your pairs of numbers, such as (3,4) look like (x,y) coordinates of points. I don't see how they define vectors. What do the numbers mean? Is O supposed to be at the origin?
drwls is right, you should be using [..,..] for vectors, so there is no confusion with ordered pairs.
Also when we say vector OA, we usually see a symbol such as --> above the OA, which of course we cannot do in this text format.
You have given OA = [2,3) so the point A is (2,3). Plot it.
Vector AB = [3,4]
Since vector OB = OA + AB
OB = [2,-3] + [3,4] = [5,1]
so point B is (5,1). Plot it.
since there is to be a right angle at B, draw a perpendicular to AB and extend it in both directions, (at this point we don't know which way it will go.)
Vector AC is to be parallel to [0,1] which means it must be parallel to the y-axis, or, it must be a vertical line.
So the x-coordinate of C must be 2.
Let C be the point (2,c)
Finally BC is perpendicular to AB
so (vector BC)∙(vector AB) = 0
[3,1-c]∙[3,4] = 0
9 + 4 - 4c = 0
c = 13/4
Plot C(2,13/4) and draw your triangle.
Finally vector OC = [2,13/4]
(you might want to check my arithmetic, I often make sloppy errors in that)
Thank you Reiny - the reason I wrote my vectors as I did was due to the notation. In our book, they are often written looking like ordered pairs - brackets not used. Thanks again!! I was on the right track, just wanted to be sure.