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Find angle between two vectors

  1. May 21, 2012 #1
    Question:
    Let u·v = 5 and u×v = 2i+3j+k. Determine the angle (in degrees to one
    decimal place) between the two vectors.

    Im not sure on what to do with the equation given since other examples that were done i was given separate equations for u and v

    We were told this formula will be used but not sure how to get u and v.
    |u x v|=|u||v|sinθ

    Thanks in advance to anyone that helps
     
  2. jcsd
  3. May 21, 2012 #2

    Andrew Mason

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    What is the value of |u x v|? From that you should be able to work out the value of tanθ and then θ without needing to find u or v.

    AM
     
  4. May 21, 2012 #3
    so, the value of |u x v|=sqrt(2^+3^+1^)?

    then substitute it so it will be |sqrt(2^+3^+1^)|=|u||v|sinθ?
     
  5. May 21, 2012 #4
    so, the value of |u x v|=sqrt(2^+3^+1^)?

    then substitute it so it will be |sqrt(2^+3^+1^)|=|u||v|sinθ?
     
  6. May 21, 2012 #5

    Curious3141

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    You're missing the exponents of 2 (squares), but yes.

    Now find a similar expression for the dot product, divide and form a simple trig equation.
     
  7. May 21, 2012 #6
    Sorry, forgot to put the exponents in.

    So will this be what it comes to...
    sinθ=sqrt(14)/5 then solve for theta?
     
    Last edited: May 21, 2012
  8. May 21, 2012 #7

    Andrew Mason

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    Not quite. You said:

    (1) uvsinθ = √14

    (2) uvcosθ = 5


    Solve for θ.

    AM
     
  9. May 22, 2012 #8

    Curious3141

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    No. Isn't there a cos θ in the definition of the dot product?

    Andrew Mason's post gives you the equations you should divide.
     
  10. May 22, 2012 #9
    so is it

    √14/sinθ=5/cosθ
    tanθ=√14/5
    θ=arctan(√14/5)?
     
  11. May 22, 2012 #10

    Curious3141

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    Yes.
     
  12. May 22, 2012 #11
    :) now i understand it.

    thank you to everyone that helped
     
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