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Homework Help 3D vectors problem solving

  1. Feb 24, 2013 #1
    Homework Help!! 3D vectors problem solving!!

    1. The problem statement, all variables and given/known data
    the vector v=(1,√2,c) makes an angle of 60° with the positive z-axis. Determine the angles that v makes with the positive x-axis and the positive y-axis. Explain how many answers there are.


    2. Relevant equations
    dot product, geometry, cosine,sine,tan


    3. The attempt at a solution
    I started by drawing the 3D vector with the x,y,z axis's and place a point on the z axis for c. I then tried using geometry with the 60 degrees and the drawn vector to find other angles and also used cosine, sine and tan with the values 1 and root 2. None of the methods seemed to work and am very confused as to what I should do next.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 24, 2013 #2

    tiny-tim

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    welcome to pf!

    hi 16leafs! welcome to pf! :smile:
    the angle between (1,√2,c) and (0,0,1) is 60°

    so use the formula for the angle between two vectors! :wink:
     
  4. Feb 24, 2013 #3

    jedishrfu

    Staff: Mentor

    Re: Homework Help!! 3D vectors problem solving!!

    start with the dot product of z dot v = |z| |v| cos (60) and recall that z is a unit vector and that cos(60) = 1/2 then solve for c

    Now can you see how many solutions for c there from the |z| |v| cos(60) equation?
     
  5. Feb 24, 2013 #4
    Re: Homework Help!! 3D vectors problem solving!!

    thanks for the replies, I really appreciate the help. I'm still confused as to why you gave c a value of unit vector one though?
     
  6. Feb 24, 2013 #5

    Dick

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    Re: Homework Help!! 3D vectors problem solving!!

    You can choose z to be any vector along the positive z axis. It doesn't really matter, but picking z=(0,0,1) would be the simplest choice, yes?
     
  7. Feb 24, 2013 #6
    Re: Homework Help!! 3D vectors problem solving!!

    The value for c would actually be different if you chose the vector [0,0,2] as for the positive z-axis. However, I believe the angles would all be the same.
     
  8. Feb 24, 2013 #7

    Dick

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    Re: Homework Help!! 3D vectors problem solving!!

    Nah, if you put z=[0,0,2] in then you get 2c in the dot product. But |z|=2. They'll just cancel out.
     
  9. Feb 24, 2013 #8
    Re: Homework Help!! 3D vectors problem solving!!

    ok (0,0,1) would seem the simplest, but how would i use the dot product method to solve for c because when i tried using (0,0,1), and then (0,0,2) i got different answers?
     
  10. Feb 24, 2013 #9
    Re: Homework Help!! 3D vectors problem solving!!

    Yup, you're right. I was doing sqrt(2) for the magnitude for some reason.

    @16leafs, you solve for c by doing

    ##[1, \sqrt{2},c] \cdot [0,0,1] = ||[1, \sqrt{2}, c] || \cdot ||[0,0,1]|| \cos{60}##
     
  11. Feb 24, 2013 #10
    Re: Homework Help!! 3D vectors problem solving!!

    When i simplify the equation, the c is cancelled out and im left with no variable?
     
  12. Feb 24, 2013 #11

    Dick

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    Re: Homework Help!! 3D vectors problem solving!!

    That's wrong. Show your work.
     
  13. Feb 24, 2013 #12
    Re: Homework Help!! 3D vectors problem solving!!

    [1,2√,c]⋅[0,0,1]= (1)(0)+(2√)(0)+(c)(1)= c

    lzl=√1^2= 1

    lvl= √(1^2+√2^2+c^2)= (√3)c

    c=(√3)c*1*cos60

    Im using equations we have used in class but it doesnt seem to work with c variable on both sides
     
  14. Feb 24, 2013 #13

    Dick

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    Re: Homework Help!! 3D vectors problem solving!!

    sqrt(1+2+c^2)=sqrt(3+c^2). That isn't equal to sqrt(3)*c.
     
  15. Feb 24, 2013 #14
    Re: Homework Help!! 3D vectors problem solving!!

    so its √3+c? giving me c=(√3+c)*1*cos60 which c's will still cancel?
     
  16. Feb 24, 2013 #15
    Re: Homework Help!! 3D vectors problem solving!!

    sorry they dont cancel. so c=√3?
     
  17. Feb 24, 2013 #16

    Dick

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    Re: Homework Help!! 3D vectors problem solving!!

    No offense, but your algebra is atrocious. You get c=sqrt(3+c^2)*1*cos(60). Figure out what cos(60) is and try to solve for c.
     
  18. Feb 24, 2013 #17
    Re: Homework Help!! 3D vectors problem solving!!

    No, √(3 + c^2) ≠ √3 + c. Just leave it as √(3 + c^2) since you cannot simplify it any more. From here, trying squaring both sides.
     
  19. Feb 24, 2013 #18
    Re: Homework Help!! 3D vectors problem solving!!

    c^2=3/2+0.5c^2

    0.5c^2=3/2

    c=√3?
     
  20. Feb 24, 2013 #19
    Re: Homework Help!! 3D vectors problem solving!!

    No, that's not right. When I said square both sides, I didn't say to ignore the 1/2 that was from the cos(60). You still need to square that. Come on!
     
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