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!

Dividing vectors?

  1. Aug 16, 2015 #1
    I have a question. Given a vector equation such as F = ma, how can we obtain a general expression for m, the mass? If the equation was scalar, this could easily be done by dividing F by a; however, we are dealing with vectors, and, to my knowledge, a vector divided by another vector is not defined in vector algebra. Therefore, how can we obtain a general expression for m?
     
  2. jcsd
  3. Aug 16, 2015 #2
    You could always just write [tex]\mathbf{F}=m \mathbf{a} \implies \mathbf{F} \cdot \mathbf{a} = m \mathbf{a} \cdot \mathbf{a} \implies \mathbf{F} \cdot \mathbf{a} = m a^2 \implies m = \frac{\mathbf{F} \cdot \mathbf{a}}{a^2}.[/tex]

    But the acceleration and the net force are always in the same direction. So the dot product is just the scalar product of the magnitudes.
     
    Last edited: Aug 16, 2015
  4. Aug 16, 2015 #3
    Take any component of F and a and you have ## F_{x_i} = m a_{x_i} ##.
     
  5. Aug 16, 2015 #4

    jbriggs444

    User Avatar
    Science Advisor

    Either pick a non-zero component or, better yet, divide the magnitudes. As long as F and a are collinear (as they must be), this will give the right answer.
     
  6. Aug 16, 2015 #5
    For the directions of ##F## and ##a## are the same, we can get
    $$\mathbf{F}=m\mathbf{a}\Rightarrow F\hat{e}=ma\hat{e}\Rightarrow F=ma \Rightarrow m=\frac{F}{a}.$$
     
  7. Aug 18, 2015 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    That last would be better written [itex]\frac{|F|}{|a|}[/itex]
     
  8. Aug 18, 2015 #7
    Sorry I used ##\mathbf{F}## as the vector force and ##F## as the magnitude of the force.
     
  9. Aug 18, 2015 #8

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Oh, I see. So you were right all along!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Dividing vectors?
  1. Divide Sphere (Replies: 2)

  2. Dividing by Infinity (Replies: 15)

  3. Dividing by Zero? (Replies: 11)

  4. Divide Two Vectors (Replies: 14)

  5. Dividing with units (Replies: 15)

Loading...