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Homework Help: Graphical Representation of Cross Product

  1. Aug 30, 2010 #1
    1. The problem statement, all variables and given/known data
    Show graphically how [tex]\vec{a}\times\vec{x}=\vec{d}[/tex] defines a line. [tex]\vec{a}[/tex] and [tex]\vec{d}[/tex] are constants. [tex]\vec{x}[/tex] is a point on the line.


    2. Relevant equations
    [tex]\vec{a}\times\vec{x}=a\cdot x\cdot sin(\theta)\cdot \hat{n}[/tex]


    3. The attempt at a solution
    Not sure if the included relevant equation is even relevant in this case. In any case, trying to graph this as a line seems impossible. Holding [tex]\vec{a}[/tex] constant and varying [tex]\vec{x}[/tex] along the line must result in different values of [tex]\vec{d}[/tex] which breaks the constraints on the original problem. It seems to me as if the above equation could only have one solution and, therefore, result in a point, not a line.

    The only way I see this working is to imply the the above equation has multiple solutions (points along the line). Is this possible? And, if so, could anyone explain it in a simple manner?.
     
    Last edited: Aug 30, 2010
  2. jcsd
  3. Aug 30, 2010 #2
    It's the line created by the vectors that have their component perpendicular to a equal to x*sin(theta) (it's not exact, the vectors must stay in a certain sense at right of a, if not they created two lines), the vector product is for definition the product of a times the component of the other vector perpendicular to a, times a certain normal vector oriented with the ax of the plane. You can draw it int this way, taken a and x, draw a parallel line to a that passes for x
     
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