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!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Differentiating Vector Products
  1. Vector product (Replies: 3)

  2. Vector product (Replies: 1)

  3. Vector products (Replies: 9)

Loading...