Expert: Abe Mantell - 5/26/2011

Question
1)The magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u: magnitude 136, bearing 220°
v: magnitude 197, bearing 300°
w: u + v

2)u: magnitude 218, bearing 22°
v: magnitude 170, bearing 112°
w: u - v

3)u: magnitude 136,. bearing 220°
v: magnitude 197, bearing 300°
w: 2u - v

Thanks so much!!

Answer
Hello Amanda,

1. In rectangular coordinates:
u=(136cos(220°),136sin(220°)) = (-104.182,-87.419)
v=(197cos(300°),197sin(300°)) = (98.5,-170.607)
Thus, u+v=(-5.682,-258.026), whose magnitude is sqrt[(-5.682)^2 + (-258.026)^2]
which is about 258.089...with reference angle arctan(258.089/5.682)=88.74°
Hence, in polar form, u+v=(258.089,180+88.74 degrees)=(258.089,268.74°)

OK?  Perhaps this is enough so you can do the other two on your own.
Give a try, if you need help with them just let me know!

Abe