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Homework Help: 'Working' with vectors

  1. Nov 7, 2004 #1
    Hello again

    I have another question!

    Suppose a particles initial position is [tex]\vec{r_1} = 2\vec{i} + 5\vec{j} - \vec{k}[/tex] metres and its acted upon by a force [tex]\vec{F} = \vec{i} + \vec{j} + \vec{k}[/tex] newtons. Its final position is [tex]\vec{r_2} = -4\vec{i} + 3\vec{j} + \vec{k}[/tex]. Find the work done by [tex]\vec{F}[/tex].

    Ok, i have the formula [tex]dW = \vec{F}.d\vec{r}[/tex] joules.

    what is dr? is it simply the change in the position vector? How do I start this off?

    Thankyou,
     
  2. jcsd
  3. Nov 7, 2004 #2

    Pyrrhus

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    Homework Helper

    It looks to me like a

    [tex] W = \int_{\vec{r}_{o}}^{\vec{r}} \vec{F} \cdot d \vec{r} [/tex]

    Use the components

    [tex] W = \int_{(r_{x_{o}},r_{y_{o}},r_{z_{o}})}^{(r_{x},r_{y},r_{z})}} (F_{x} \vec{i} + F_{y} \vec{j} + F_{z} \vec{k}) \cdot (dr_{x} \vec{i} + dr_{y} \vec{j} + dr_{z} \vec{k}) [/tex]
     
    Last edited: Nov 7, 2004
  4. Nov 7, 2004 #3
    Thankyou very much
     
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