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: Cross product derivative

  1. Feb 5, 2007 #1
    hi all.

    my homework question is what is the derivative of:

    [(a + t * b) x (a + t * b + t^(2) * c)]

    a, b, and c are vectors, and t is a constant. * is multipy, ^(2) is squared, and x is cross product.

    i've been working on it for hours and i have no idea what to do.

    there's another similar problem which i have the answer to. it asks to find the derivative of:

    [(a + t * b) x (c + t * d)]

    it has the same specs, with d being another vector.

    the answer to this one is:

    (a x d) + (b x c) + 2t(b x d)

    i just don't see how these connect and can actually be equivalent.

    help would be ridiculously appreciated.
  2. jcsd
  3. Feb 5, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You have a (cross) product there. So you should use the (cross) product rule.
  4. Feb 6, 2007 #3


    User Avatar
    Science Advisor

    First, the product rule, for cross product: (uxv)'= uxv'+ u'xv.

    Second, cross product is anti-commutative: uxv= -vxu and, in particular, uxu= 0.
    Finally, cross product is distributive: ux(v+ w)= uxv+ uxw (though is it NOT associative).

    Look at your second, simpler, problem: [(a + t * b) x (c + t * d)] '
    = (a+ tb)' x(c+ td)+ (a+tb)x(c+ td)'= bx(c+td)+ (a+tb)x(d)= bxc+ t(bxd)+ axd+ t(bxd)= axd+ bxc+ 2t(bxd).
    Last edited by a moderator: Feb 6, 2007
  5. Feb 6, 2007 #4
    ok thank you so much you two.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook