Help with vectors?

For the vectors given in Fig. 3-32 (|A| = 55.0 and theta= 53.0°), determine the following.





http://www.webassign.net/giancoli5/3_35a...





(a) A - B + C


Magnitude____


Direction____° (counterclockwise from the +x axis is positive)





(b) A + B - C


Magnitude____


Direction____° (counterclockwise from the +x axis is positive)





(c) C - A - B


Magnitude____


Direction____° (counterclockwise from the +x axis is positive)

Help with vectors?
The easiest way to do problems like this is to break the vectors into their components.


Ax = Acos28 = 48.56, Ay = A sin28 = 25.82


Bx = -Bcostheta = -24.07 By = 31.95


Cx = 0 Cy = -46.8





Ok, now that we've done that it will be easy to find the x and y components of the resultant vector.





So for a) A - B + C = R


Rx = 48.56 - -24.07 + 0 = 72.63


Ry = 25.83 - 31.95 - - 46.8 = 40.68





Magnitude = (Rx^2 + Ry^2)^0.5 = 83.2


Direction = theta = tan-1(Ry/Rx) = 29.3 degrees





You have to be careful if Rx or Ry is negative because that puts you into a differenct quadrant. I usually draw a picture of where the vector is, use the inverse tangent function (arctan) as I did above with only the positive values. That will always be the angle the resultant makes with the closest x-axis. Then from there I figure out what the angle I need is given that there are 360 degrees altogether.





I think you're set to do parts b and c!