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Basic Vectors Equation

  1. Apr 20, 2009 #1
    1. The problem statement, all variables and given/known data

    Two vectors are given by Avec = -1 i + 2 j and Bvec = 4 i + 2 j

    Find A X B

    Find the angle between A and B


    3. The attempt at a solution

    Okay well I got the First part of the problem, I know that A X B is -10, but when I do everything for the angle I keep getting the wrong answer.

    After I finish with my calculating I come up with cos (theta) = -10/10 which would simplify to 180 degrees, but thats wrong...

    Can someone please help me out, I dont understand where im going wrong

    Thank You!
     
  2. jcsd
  3. Apr 20, 2009 #2
    If you want the cosine of the angle you need the dot product (not the cross product).
    The angle is 90 deg, the two vectors are perpendicular.

    If you use the cross product, you'll get sin (theta)=1 and theta = 90 deg.
     
  4. Apr 20, 2009 #3
    oo ok, thank you
     
  5. Apr 20, 2009 #4
    It's important to remember how the cross-product is defined before you look at this problem. The cross-product is an operation in a 3-D vector space that produces a third vector.

    In this case:
    (-1, 2, 0) [tex]\times[/tex] (4, 2, 0) = (0, 0, -10)

    The cross product also gives you:
    [tex]a \times b = \sin{\theta} \nhat[/tex]

    You might have an easier time looking at the dot product only.

    But if your 2D vectors aren't actually lying in a 3D space, do not use the cross product at all, as it is not well defined.
     
    Last edited: Apr 20, 2009
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