1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook