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Homework Statement
Show that if σ(t) for (t in I) is a parametrization of a line, then σ''(t) is parallel to σ'(t).
Homework Equations
The Attempt at a Solution
I thought that if σ(t) is a parametrization of a line then it could be expressed as σ(t) = vt + a, but then σ'(t) = v and σ''(t) = 0. Can two vectors be parallel? Is it because the distance between them is constant? Or did I make a mistake earlier on?