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Homework Help: Some EM1 vector problems

  1. Sep 10, 2005 #1
    I'm using wangsness EM book. I keep doing ch 1 #5 and keep getting 19, despite the back of the book saying -14.4

    A = <2,3,-4>
    B = <-6,-4,1>

    AxB = <-13, -22, 10> = D

    Find the component of AXB along the direction of Vector C

    C = <1,-1,1>

    Now im using

    CD = CDcos(theta)

    Im getting 66.4º

    Now, to get the component I used:

    Magnitude = DCcos(66.4)

    Does this method make sense?
     
  2. jcsd
  3. Sep 10, 2005 #2

    Doc Al

    User Avatar

    Staff: Mentor

    To get the component of D in the direction of C, you need to take the dot product of D with the unit vector in the direction of C. (Divide [itex]\vec{D} \bullet \Vec{C}[/itex] by the magnitude of C.)

    (Also: Why mess around with angles when you have the components?)
     
  4. Sep 11, 2005 #3
    Thanks for the help, I tend to do things the hard way. I have another question:

    "A family of hyperbolas in the xy plane is given by u = xy. Find the gradient of u. Given vector A = 3i + 2j + 4k find the component of A in the direction of gradient u at the point u = 3 and x = 2"

    Since we know that u = 3 and x = 2, we can gather that the point of the hyperbola is x =2 and y = 3/2

    Lets call this vector E

    so E = 2i + (3/2)j + 0k

    This problem is similiar to the previous one I asked, finding the component. So I take it since I want to find the component of A in the direction of Grad U, I will need to make E into a unit vector

    U = (4/5)i + (3/5)j + 0k

    Now I presume I dot U and A?

    That would create

    UA = (8/5) +(9/10) = 5/2
     
  5. Sep 11, 2005 #4
    Ignore the previous post. I was experiencing brain drain...
     
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