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Dot Products

  1. Oct 18, 2004 #1
    I need some major help with some dot products. I was curious if when getting the dot product, you add the angles of each one to each other. I'll give the problem:

    theta=(/)

    Find A*B(dot product)
    A=8.6i+5j
    B=9.7i+2.6j

    So i used the formula my teacher gave me to find the angle, theta, tan(/)=y/x. So i got the Angle for each:
    tan(/)=5/8.6
    (/)=tan^-1(5/8.6)
    (/)=30.2

    and then for B:
    tan(/)=2.6/9.7
    (/)=tan^-1(2.6/9.7)
    (/)=15

    So now, I am given two formulas to get the dot product
    A*B=ABcos(/)
    AB means the magnitude of A multiplied by the magnitude of B. I can get that, but it asks for one angle... what do I do? Add the two angles together? Or subtract them? I'm confused, please help!
     
  2. jcsd
  3. Oct 18, 2004 #2

    chroot

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    Gold Member

    In the formula

    [tex]\vec A \cdot \vec B = || \vec A || \, || \vec B || \cos \theta[/tex]

    the angle [itex]\theta[/itex] is the angle between the two vectors. When you found the "angle" for each vector, what you were really finding was the angle between each vector and the positive x-axis. If one vector makes an angle of 30.2 degress with the positive x-axis, and the other makes an angle of 15 degrees, the angle between them is 30.2 - 15 = 15.2 degrees.

    When it doubt, draw a picture! You'll see that the two vectors make an angle of 15.2 degrees between them.

    - Warren
     
  4. Oct 18, 2004 #3

    NateTG

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    For the lazy among us, there's an alternative formula:
    if
    [tex]\vec{A}=<A_x,A_y>[/tex]
    and
    [tex]\vec{B}=<B_x,B_y>[/tex]
    then
    [tex]\vec{A}\cdot\vec{B}=A_xB_x+A_yB_y[/tex]
     
  5. Oct 18, 2004 #4
    I use both formulas, the first that Warren mentioned to get the answer, then i use the lazy way to check it. Thanks guys!
     
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