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Homework Help: How to find the angle between an XYZ vector and the y-axis? Please help

  1. Feb 4, 2010 #1
    How to find the angle between an XYZ vector and the y-axis? Please help!!!

    1. The problem statement, all variables and given/known data

    A vector is given as follows:

    A = 2i - 2j - 3k

    The angle between A and the y-axis is, in degrees, closest to?:

    90
    119
    151
    61
    29

    2. Relevant equations

    c = ab sin[tex]\theta[/tex] ????

    3. The attempt at a solution

    I tried:

    cos[tex]\theta[/tex] = (AdotB)/(A x B)

    I tried to set a vector along the y-axis to use as B.

    Isolating [tex]\theta[/tex] yielded 56.3 degrees, which is apparently incorrect.
     
  2. jcsd
  3. Feb 4, 2010 #2

    berkeman

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    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    Maybe try using the cross-product instead of the dot-product...
     
  4. Feb 4, 2010 #3
    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    To be honest, I don't know what formula to use and I don't even know if I can use the y-axis as a vector.

    I don't want the answer... I just want to know where to start and what procedure I should use.

    I'm pretty confused.
     
  5. Feb 4, 2010 #4

    vela

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    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    You're just mixing up the dot product and the cross product. You should have

    [tex]\vec{A}\cdot\vec{B} = |A||B|\cos \theta[/tex]
    [tex]|\vec{A}\times\vec{B}| = |A||B|\sin \theta[/tex]

    You can use either to find the angle [itex]\theta[/itex].
     
  6. Feb 4, 2010 #5

    berkeman

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    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    The unit vector in the direction of the y-axis is the j vector. Do you know the equation for the vector cross-product? How could you perhaps use it to find the angle?
     
  7. Feb 4, 2010 #6
    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    Well like vela posted the cross-product formula is LaTeX Code: [tex]|\vec{A} X \vec{B}| = |A||B|sin \theta [/tex]

    But I only have a vector A? Or can I use components of vector A in that formula?
     
    Last edited by a moderator: Feb 4, 2010
  8. Feb 4, 2010 #7

    berkeman

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    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    I tried to clean up your latex -- hope I got it right.

    Since you are asked to find the angle with the y axis, you have two vectors. you have A, and you have j. If you cross A into j as vectors, you will get an answer that has the inclusive angle in it. Do you know how to calculate the cross-product using a determinant?
     
  9. Feb 4, 2010 #8
    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    That part I do know how to do. But if I crossed vectors A and j, wouldn't I just get a vector in some form of i + j + k? How would I calculate an angle from that?
     
  10. Feb 4, 2010 #9

    berkeman

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    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    Use the magnitude equation that you posted a couple steps back. The magnitude of the vector resultant is related to the magnitude of A and j and ...
     
  11. Feb 4, 2010 #10
    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    Ahh, of sintheta

    I'm getting it now.

    Is j = (0i -2j + 0k)? Is it as simple as that?
     
  12. Feb 4, 2010 #11
    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    I tried to solve it as such... and I got 61 degrees which was wrong...
     
  13. Feb 4, 2010 #12

    berkeman

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    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    Post the details of your calculation. Also, make a good sketch for yourself in 3-space, to get an intuitive feel for what the answer should be.
     
  14. Feb 4, 2010 #13
    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    A = 2i - 2j - 3k ... A = 4.12
    j = 0 + 1j + 0 ... j = 1
    Code (Text):

    |i   j   k |
    |2  -2  -3 |
    |0   1   0 |...... this matrix yielded [B]N[/B] = 3i + 2k ... N = 3.61
     
    N = Aj sintheta
    theta = sin^(-1) (N/Aj) = 61 degrees
     
    Last edited by a moderator: Feb 4, 2010
  15. Feb 4, 2010 #14

    berkeman

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    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    Yeah, I get the same answer. It's not right? Do they want a couple figures to the right of the decimal point maybe?
     
  16. Feb 4, 2010 #15

    berkeman

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    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    Oops, I see it's multiple choice. What does it look like in your sketch?
     
  17. Feb 4, 2010 #16
    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    It's a multiple choice problem with the choices being:

    90
    119
    151
    61
    29

    I've already tried 2 answers, forfeiting 50% of the potential credit. Is it possible that it is 151 degrees? That is 61+90 degrees... Or 119? 180 - 61?

    God I hate Mastering Physics. They gave us a free trial for it as LSU. What's the catch? We're basically beta testers. Infuriating.
     
  18. Feb 4, 2010 #17
    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    I'm bad at sketching 3d and I really don't know how to interpret my sketch.
     
  19. Feb 4, 2010 #18

    berkeman

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    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    I think the sketch is needed to see the answer. It's over 90 degrees to the positive y axis... Since the answer is multi-valued, our calculators only gave us the value for the first quadrant of the sine function...
     
  20. Feb 4, 2010 #19
    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    Eh, I am bad at sketching in 3d. What can I say about it really? It's below the XY plane?

    Exactly what is theta in this case?
     
  21. Feb 4, 2010 #20
    Re: How to find the angle between an XYZ vector and the y-axis? Please help!!!

    The answer was 119 apparently. I don't even know why. Maybe my sketch is just extremely difficult to interpret? Blah.

    Anyway, thanks for the time and input. At least I have the raw calculation part down.

    Thanks a bunch.
     
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