Finding X2' and Y2' from Vector Values

  • Thread starter MatrixGL
  • Start date
  • Tags
    Vector
In summary, To find the coordinates (x2', y2') from given values (x, y), (x', y'), and θ, you can use polar coordinates or set up two equations using the fact that both (x', y') and (x2', y2') lie on the same circle, and the given angle θ. Another approach is to use a triangle with two equal sides and the given angle to determine the angle at (x', y'), and then set up a dot product between two suitable vectors to get a second equation.
  • #1
MatrixGL
5
0
44bbqqx.gif


It's been a while since I've been in a math class. I'm just trying to make a simple openGL demo, and I ran into this problem.

If you look at the picture, I know the values of:

x, y
x', y'
θ

Now, from those, how can I find X2' and Y2' on a cartesian coordinate system?

lol, the question might seem dumb, but I've been out of touch for a long time and while I've done some searches I did not find anything specific.

Any help would be greatly appreciated!

Thanks!
 
Mathematics news on Phys.org
  • #2
Use polar coordinates.

You can find r and angle (of x' and y'), say phi, with (x,y) and (x',y'). r is going to be the same for (x2', y2') and you know the angle, which is phi+theta. So use r and theta+phi to determine x2' and y2'.
 
  • #3
If you don't want to use polar coordinates, you might do it this way:
You need 2 equations to determine (x2,y2), so what could work?

1. Both (x',y') and (x2,y2) lie on the SAME circle.
What equation can represent this fact?

2. We may determine the angle at (x',y'):
Having a triangle with two equal sides and a given angle should give us this angle.

3. Set up a dot product between two suitable vectors!
This gives you a second equation, along with the circle equation.
 

1. How do you find X2 and Y2 from vector values?

To find X2 and Y2 from vector values, you can use the Pythagorean theorem. X2 can be found by taking the square root of (X1^2 + Y1^2), where X1 and Y1 are the initial vector values. Y2 can be found by taking the square root of (X1^2 + Y1^2), where X1 and Y1 are the initial vector values. Alternatively, you can use trigonometric functions to find X2 and Y2.

2. What are vector values?

Vector values are quantities that have both magnitude and direction. They can be represented graphically as arrows, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

3. Can you find X2 and Y2 from just one vector value?

No, X2 and Y2 cannot be found from just one vector value. X2 and Y2 are the components of the vector, and both components are needed to calculate the final values.

4. Are there different methods for finding X2 and Y2 from vector values?

Yes, there are different methods for finding X2 and Y2 from vector values. The most common methods involve using the Pythagorean theorem or trigonometric functions, but there may be other methods depending on the specific problem.

5. Can vector values be negative?

Yes, vector values can be negative. Negative vector values indicate a direction opposite to the positive direction. In graphical representations, a negative vector value would be represented by an arrow pointing in the opposite direction. However, when using mathematical equations to find X2 and Y2, it is important to use the correct signs for the vector values.

Similar threads

Replies
2
Views
1K
Replies
12
Views
2K
  • General Math
Replies
3
Views
881
Replies
1
Views
623
  • General Math
Replies
11
Views
1K
Replies
2
Views
1K
Replies
1
Views
1K
Replies
76
Views
4K
Replies
11
Views
6K
Back
Top