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Homework Help: Dot product between two unit vectors

  1. Nov 25, 2011 #1
    Hello, I am trying to find the angle between two unit vectors but I was wondering what I am supposed to do when the dot product is greater than 1 or less than -1.

    For example

    -0.0288067i + -0.989524j + -0.141463k
    0.169194i + -0.0644865j + -0.983471k
  2. jcsd
  3. Nov 25, 2011 #2
    The unit vectors [itex]\underline{i}[/itex],[itex]\underline{j}[/itex]and [itex]\underline{k}[/itex] all are at right angles to each other just like the x,y,and z co-ordinate axes.

    Does your difficulty refer to the angle between two vectors which are not unit vectors?
  4. Nov 25, 2011 #3
    The problem is that the dot product between the two vectors I mentioned above is less than -1, and that won't let me calculate the arccosine. I was wondering if there's another way of calculating the angle between them.
  5. Nov 25, 2011 #4
    Nevermind !
  6. Nov 25, 2011 #5
    costheta = (v1 dot v2)/(magnitude of v1*magnitude of v2)

    The above will always be greater than -1 and less than +1.
  7. Nov 25, 2011 #6
    I'm sorry but once again, how would you deal with this vector?

    0.444119i + 0.666155j + 0.599163k
    -0.0587215i + 0.732467j + 0.678265k

    the dot product is 1.73928, and the magnitude of each vector is 1. How do you calculate the angle between them? :(
  8. Nov 25, 2011 #7
    Are you sure? I get a dot product of 0.868249 for these vectors, and 0.198062 for the vectors in your first post.
  9. Nov 25, 2011 #8


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    Science Advisor

    It looks like you are just doing the dot product wrong. I get
    (-0.0260793338585)+ (0.487936554385)+ (0.406391292195)= 0.8682485127215
    just as Rasalhaque did.

    Perhaps if you showed more detail on how you are doing the dot product we could see where your error is.
  10. Nov 25, 2011 #9
    Was this problem given as a 'punishment'? It is so tedious to calculate!

    You must have a mistake in the calculations.

    There is NO WAY that (v1 dot v2)/(magnitude of v1*magnitude of v2) is greater than 1 or less than -1.
  11. Nov 25, 2011 #10
    I have a feeling that Marioque is enjoying seeing us calculating!!
  12. Nov 25, 2011 #11
    I also got 0.8682484 for the dot product.
  13. Nov 25, 2011 #12
    jaja! grzz. It was my mistake again :(. No more dumb questions. I'm really sorry.
  14. Nov 25, 2011 #13
    No need to be sorry. Sometimes I myself make mistakes.

    My maxim is:

    One may sometimes swallow some water but that is the way one learns to swim!

    Enjoy your 'swimming' in PhysicsForums!
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