1. Not finding help here? Sign up for a free 30min 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!

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

    Mark44

    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

    Mark44

    Staff: Mentor

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    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].
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Derivative of Vector Function
Loading...