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Homework Help: Differentiating Vector Products

  1. Mar 8, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove that d/dt[r.(vxa)] = r.(vxda/dt)

    2. Relevant equations

    r, v, a are position, velocity and acceleration vectors.
    ..r.(v.. is the dot product.
    ..vxa.. is the cross product

    3. The attempt at a solution

    I expand the equation using the product rule for dot and cross products to get:

    dr/dt.(vxa)+r.(dv/dt x a+v x da/dt)

    I've expanded this further on paper using the x,y,z components of each vector but i can't manipulate it to get the desired result? Have I missed a step or overlooked something here?
  2. jcsd
  3. Mar 8, 2012 #2
    well its way more simple than you are assuming. derivative of v with respect to time is a, so your second term is a cross product between a and a, so that becomes zero. In the first term, the time derivative of r is v. So it becomes
    [itex]\mathbf{v}\cdot (\mathbf{v}\times \mathbf{a})[/itex] Use the property of vector triple product to make this zero. So you are left with the last term
    Last edited: Mar 8, 2012
  4. Mar 9, 2012 #3
    Thanks very much.
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