[anastacia]

Hello to whomever reads this message,
    The exact problem states:  At low temperatures a substituted 1,2-dichloroethane molecule can adopt 3 conformations-(shown as para, and 2 meta's- cl at the top and another cl to the left for one and the right for the other) with different probabilities.  Suppose the dipole moment of each bond is 1.5 D.  Calculate the mean dipole of the molecule when a) all 3 conformations are equally likely, b)only the meta with cl on top and another cl to the right(on a newman projection) occurs, c)the 3 conformations occur w/ probabilities of 2:1:1 d)1:2:2.  Answers:  1.5D, 2.6D, 1.13D,1.8D.  I believe I found the answer to part b in the following manner:  
ux=1.5cos(30)+1.5cos(90)=1.299
uy=1.5sin(30)+1.5sin(90)=2.25
u=(1.299^2+2.25^2)^.5=2.6D
Please help if possible.  Thank you for your time.
Anastacia- email:anastace@umich.edu

[Demotivator]

Ok, your result for b looks corrrect.
For a, all conformations likely, the x components do not contribute because they cancel out for the two metas. That leaves only y components. Note that for para conformer, the y components cancel to 0 and x is also 0.:
(0 + (.75+1.5) + (.75+1.5)) /3 =1.5  which matches the given answer.

Now, The mean is based on a weighted average (and 1.5sin30 = .75 etc):
2:1:1 -- The x components  cancel:
ux = (2(0) +(1.299) - 1.299 )/4 = 0
uy = (2(0) +(1.5+.75) + (1.5+.75))/4 = 1.13
u=(0^2 + 1.13^2)^.5 = 1.13 D

1:2:2  The x components  cancel:
ux = (0 + 2(1.299) - 2(1.299))/5 = 0
uy = (0 + 2(1.5+.75) + 2(1.5+.75))/5 = 1.8
u=uy = 1.8 D