If $${C}$$ is the straight line that connects points in the plane $${(x_i, y_i)}$$ and $${(x_f, y_f)}$$, find a path $${\tmmathbf{r} (t)}$$ that traces out $${C}$$ starting at the initial point $${(x_i, y_i)}$$ and ending at $${(x_f, y_f)}$$ as $${t}$$ goes from zero to 1.(adsbygoogle = window.adsbygoogle || []).push({});

Now the path that I've been able to come up with is

r=(xf-xi)cos(t) i +(yf-yi)sin(t) j

Note r is a vector giving the path and i and j are the unit vectors.

Is my path correct or is their some error in it?

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# Setting up a path for a line integral

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