The triangle ABC is defined by the following information. Vector OA = (2, -3), vector AB = (3, 4), AB and BC are perpendicular, and vector AC is parallel to (0, 1). Draw a diagram of triangle ABC. Write down the vector OC.
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.
To draw the diagram of triangle ABC, follow these steps:
1. Start by drawing the point O at coordinates (2, -3).
2. From point O, draw vector OA with coordinates (2, -3).
3. Place point A at the endpoint of vector OA.
4. Draw vector AB with coordinates (3, 4) starting from point A.
5. Make sure AB and BC are perpendicular. To do this, draw a line perpendicular to AB starting from point B. This line should intersect AB at a right angle.
6. Label the intersection point between the perpendicular line and AB as point C.
7. Complete the triangle by connecting points A and C with segment AC and connecting points B and C with segment BC.
Now, to find the vector OC:
Vector OC can be found by adding the vectors OA and AC together.
OA = (2, -3) and AC is parallel to (0, 1).
Since AC is parallel to (0, 1), it means that both vectors have the same direction.
Therefore, vector AC has the same coordinates as vector OA, but the magnitude can be different.
Thus, the vector OC would have the same coordinates as vector OA, which is (2, -3).