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January 20, 2017
Posted by **Wanda** on Saturday, March 29, 2008 at 3:02am.

- IB Math SL -
**drwls**, Saturday, March 29, 2008 at 6:41amYour 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?

- IB Math SL -
**Reiny**, Saturday, March 29, 2008 at 8:01amdrwls 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) - IB Math SL -
**Wanda**, Saturday, March 29, 2008 at 2:27pmThank 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.