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Angles between vectors

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  1. Jun 19, 2017 #1
    1. The problem statement, all variables and given/known data
    From Analytical Mechanics by Grant R. Fowles & George L. Cassiday.
    6rSwBZ0.png
    Only problem I am having is with part d.
    2. Relevant equations
    ##A\cdot B = A_xB_x+A_yB_y+A_zB_z##
    ##sin(\theta) = \frac{|A\times B|}{AB}##

    3. The attempt at a solution
    y2IqTYi.png
    I did it by hand but also ran the following Matlab script:
    Code (Matlab M):

    A = [1,1,1];
    B = [1,1,0];
    theta = acos(dot(A,B)/norm(A)/norm(B))
    theta = asin(norm(cross(A,B))/norm(A)/norm(B))
     
    Both formulas return 0.61548. I think the minus sign in part d should not be there, but I might be missing something. A second pair of eyes would be appreciated.
     
  2. jcsd
  3. Jun 19, 2017 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Where do you get the 1-1 in the numerator from?

    (1*1)+(1*1)+(1*0)=1+1.

    You can also use the result of (c) to get the angle.
    (c) doesn't look like a final answer by the way.
     
  4. Jun 19, 2017 #3
    The image is the solution from the manual. I used the Matlab code and got and angle of .6 in radians. It appears the solution manual was incorrect.
     
  5. Jun 19, 2017 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Yes, the solution shown in the second image is wrong.
     
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