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Homework help on vectors please

  1. Jun 1, 2016 #1
    1. The problem statement, all variables and given/known data
    http://imgur.com/a/Yq8pW


    2. Relevant equations
    projection u onto v: ((u x v)/(||v||^2)) x v
    Unit vector: u/||u||

    3. The attempt at a solution

    For number 2, I absolutely do not know how to set up the problem. I do not know what vectors to use, I assumed F vector to be <0.00375, 0.00625> and v vector to be <3 , 5> and plug them into the projection formula- projection u onto v: ((u x v)/(||v||^2)) x v-but that seems wrong since the teacher addressed that I find the vector of V, magnitude of vector V, and find unit vector so it should be <3, 5>/(sqrt 34) but how do I find the angle off of that?
     
  2. jcsd
  3. Jun 1, 2016 #2

    jedishrfu

    Staff: Mentor

    Do you know about the vector dot product and what it represents?
     
  4. Jun 1, 2016 #3
    I can find the angle between the vectors. Yes? But what I am confused about is what vectors to use.
     
  5. Jun 1, 2016 #4

    jedishrfu

    Staff: Mentor

    You have F in i,j,k form and you should have v in i,j,k form.
     
  6. Jun 1, 2016 #5
    I think I got it! Except that the question states that the vector V is in the xy plane:
    cos^-1((<3 , 5> x <0.00375 , 0.00625>)/(sqrt34 x sqrt 50))=89.94
     
  7. Jun 1, 2016 #6

    jedishrfu

    Staff: Mentor

    Vector F=<3,5,4>/sqrt(3^2 + 5^2 + 4^2) * 800

    so the unit vector for F is: Funit=<3,5,4> / sqrt(3^2 + 5^2 + 4^2) = <3,5,4> / (5*sqrt(2))

    and unit vector Vunit = <3,5,0> / sqrt(3^2 + 5^2 + 0^2) = <3,5,0> / sqrt(34)

    Funit . Vunit = (3^2 + 5^2 + 0*4) / (5*sqrt(2)*sqrt(34))

    I didn't get 89.94 degrees for the angle.
     
  8. Jun 1, 2016 #7
    Did not realize I had to multiply my F vector by 800. And based on your solution, the angle is found to be 34.4. Thanks much!
     
  9. Jun 1, 2016 #8

    jedishrfu

    Staff: Mentor

    In this case, there was a shortcut way too. If you notice that F, v and the 4k z component of F form a right triangle with F as the hypotenuse so that the sin of the angle must be 4/magnitude(F) = 4/sqrt(50) and hence its 34.4 degrees.
     
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