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Determine a formula for (RE: vector valued functions)

  1. Apr 22, 2008 #1
    Let r(t) be a v.v.f -with the first and second derivatives r' and r''. Determine formula for
    d/dt [r.(r' x r'')] -in terms of r:

    How do we approach this one?

    d/dt [r.(r' x r'')] = d/dt [r.r' x r.r''] = ((r'.r' + r.r'') x r'.r'') + (r.r' x (r'.r'' + r.r''')) ??
    ...and then what?

    Is anyone able to give me a starting point -- or starting direction? -- thanks heaps
  2. jcsd
  3. Apr 22, 2008 #2


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    Staff Emeritus
    Science Advisor

    What you have now doesn't make sense. r.r' is a number, not a vector. Same thing for r.r". You can't take the cross product. You seem to be assuming that u.(v x w)= (u.v)x(u.w) and, as I just said, that product doesn't make sense.

    How about jusst using the product rule:
    d/dt[r.(r' x r")]= r'.(r'x r")+ r.(r'+ r")'. The first term is easy: (r' x r") is perpendicular to both r' and r" so its dot product with r' is ???

    Now expand (r' x r")' in the same way. Again, the first part of the sum is trivial.
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