SOLUTION: Given the magnitudes of vectors u and v and the angle theta between them, find the magnitude of the sum u+v? and the angle that the sum vector makes with u to the nearest degree. |

Algebra ->  Vectors -> SOLUTION: Given the magnitudes of vectors u and v and the angle theta between them, find the magnitude of the sum u+v? and the angle that the sum vector makes with u to the nearest degree. |      Log On


   

Question 928441: Given the magnitudes of vectors u and v and the angle theta between them, find the magnitude of the sum u+v? and the angle that the sum vector makes with u to the nearest degree. |u|=57, |v|=57, theta=12 degree
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look at the components of each vector.
u=(57,0)
v=(57cos%2812%29,57sin%2812%29)
Adding them,
u+v=(57%2B57cos%2812%29,0%2B57sin%2812%29)
u+v=(57%2B57cos%2812%29,57sin%2812%29)
or approximately
u+v=(112.75,11.85)
So then the magnitude is,
abs%28u%2Bv%29=sqrt%28112.75%5E2%2B11.85%5E2%29
abs%28u%2Bv%29=113.4
The angle is that u+v makes with u is 1/2 the original angle, alpha=6