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Homework Help: Derivative of Vector Function

  1. Oct 6, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the derivative of the vector function
    r(t)=ta X (b+at)
    where a=<4,5,2>, b=<1,-3,2>, and c=<4,3,1>

    2. Relevant equations

    3. The attempt at a solution
    I know how to take the derivative and everything but the way this question is worded confuses me!
    I'm assuming the X means cross product? but it may just mean multiply. Do I plug in the values of a,b,c, and then do what with all the t's?
  2. jcsd
  3. Oct 6, 2009 #2


    Staff: Mentor

    I'm pretty sure X means cross product. People generally don't use X to mean ordinary multiplication at the calculus level.

    Yes, substitute the values for a, b, and c, and then carry out the cross product. You'll end up with either (...)i + (...)j + (...)k or <..., ..., ...>, both of which will have terms with t in them. To get r'(t), just take the derivative of each of the three components.
  4. Oct 6, 2009 #3
    should I distribute the t to the a values?
  5. Oct 6, 2009 #4


    Staff: Mentor

    Yes. t is a scalar, so ta = <4t, 5t, 2t>. at is the same as ta.
  6. Oct 7, 2009 #5


    User Avatar
    Science Advisor

    Don't carry out the product! Just use the product rule for vector multiplication:
    [itex]\vec{f}= \vec{a}t\times (\vec{b}+\vec{c}t[/itex])

    so [itex]\vec{f}'= \vec{a}\times (\vec{b}+ \vec{c}t)+ \vec{a}t \times \vec{c}= \vec{a}\times\vec{b}+ 2\vec{a}\times\vec{c}t[/itex].
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