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I Constructing a vector from a point

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  1. Aug 29, 2016 #1
    So I have solved the following problem: Consider two points located at ##\vec{r}_1## and ##\vec{r}_2##, separated by distance ##r = |\vec{r}_1 - \vec{r}_2|##. Find a vector ##\vec{A}## from the origin to a point on the line between ##\vec{r}_1## and at ##\vec{r}_2## at a distance ##xr## from the point at ##\vec{r}_1## where ##x## is some number.

    So I have solved this problem. The answer is ##\vec{A} = (1 - x) \vec{r}_1 + x \vec{r}_2##. I did this by allowing ##\vec{r}## to vary with ##x##, and then ##\vec{A}## was just the vector sum of ##\vec{r}_1## and ##x \vec{r}##. However, I am not really understanding the solution. When we substitute 0 for x, we find that we get ##\vec{A} = \vec{r}_1##, as expected. However, when we substitute r for x, we don't get ##\vec{r}_2##. What is going on here?
     
  2. jcsd
  3. Aug 29, 2016 #2

    pwsnafu

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    ##A = r_2## when ##x = 1##. The question says "at a distance ##xr## from ##r_1##", so when ##x=1## you are distance r from ##r_1## which is ##r_2##.
     
  4. Aug 29, 2016 #3
    Oh wow, that is pretty obvious now. Thanks!
     
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