How i find vectors from the sum of their magnitudes?

Oct 2011
4
0
if I have ||u + v|| = 3 and ||u - v|| = 7. I have to find u.v,
¿how i find "u" and "v"?

thank you very much!
 

mathman

Forum Staff
May 2007
6,932
774
|u+v|^2 = |u|^2 + 2u.v +|v|^2

|u-v|^2 = |u|^2 - 2u.v +|v|^2

Take the difference between the two equations.

|u+v|^2 - |u-v|^2 = 4u.v
 

HallsofIvy

Math Team
Sep 2007
2,409
6
Notice that the answer to your question "How do I find u and v" is "you can't". Fortunately, you don't have to find them to answer your real question.