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Linear Vector function of a vector

  1. Jun 18, 2008 #1
    1. The problem statement, all variables and given/known data
    For each state wheather the function is a linear vector function of [tex] \vec{v} [/tex]


    2. Relevant equations
    1.[tex] \vec{F}(\vec{v})=\alpha \vec{v} [/tex]
    2. [tex] \vec{F}(\vec{v})= \vec{a} \times (\vec{b} \times \vec{v}) + (\vec{a} \times \vec{v}) \times \vec{v}[/tex]


    3. The attempt at a solution
    I don't get what they mean. The book makes it look ambigious.
     
  2. jcsd
  3. Jun 18, 2008 #2
    They make what look ambiguous? The definition of a linear function? A linear function is a function f such that

    [tex]f(\vec{x}+\vec{y})=f(\vec{x})+f(\vec{y})[/tex]
    [tex]f(a\vec{x})=af(\vec{x}).[/tex]​

    Edit: Or, are you not sure what they mean by F being a function of v?

    B.T.W., do you know the formula for the vector triple product?
     
  4. Jun 18, 2008 #3
    Actually I get it, it was presented differently in the book. It's all so trivial now. And yes I do know the formula for a triple product
     
  5. Jun 18, 2008 #4
    great!
     
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