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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# I Constructing a vector from a point

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