Solving vector problems with geogebra
Take a look at the problem over here:
http://www.mathisfunforum.com/viewtopic … 17#p168917
We want to solve for P and Q. We want to solve this using Geogebra.
Define the origin as A
Start by putting in the initial vectors. On the command line enter:
u = (0,-5)
Now create a point at (-8 , 0 ) called B. Get the angle of B and A of 15 degrees. That point will be called B'. Draw a vector from A to B' it should be called v. It will have a magnitude of 8 N.
Add the two vectors u and v by inputting u + v in the command line. It should be called w or w'. Negate that vector to reflect it into the first quadrant by inputting:
w = -w'
This is the reflection vector.
Put a point at ( 0 , 8 ) called C. Create an angle of 20 degrees using C and A. That will reate the point C'. Draw a vector from A to C'. Relabel C' to Q.
Create a vector from A to ( 8 , 0 ) and call it P. Get the resultant of P and Q by adding in the command the name of two vectors they will be small letters. On mine they are a,z
a + z
The resultant is called b. Recolor this b vector red. Now move P ( the head of the horizontal vector ) towards A until it covers the reflection vector from the 3rd quadrant.
Now if you drag C (0,8) towards A the red vector c will shorten. Keep adjusting P and C until the red vector exactly superimposes over the reflection vector.
When you eyeballed it as best you can measure the distance between A and Q and A and P. I get Q = 7.55 and P = 5.18 That is quite close.
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.