# vector valued function/parametric equation of a line

Here's the set up of the problem:

Let $r(t)=<at, bt, ct>$ be a vector valued function. This is the equation of a line going through the origin of $\mathbb{R}^3$.

The problem (taken from a calculus book) asks to show that the angle between $r(t)$ and $r'(t)$ is constant.

I think that the problem as stated in the book is false: since $r'(t)= <a, b, c>$ then using the dot product we get that $cos(\alpha)= \frac{t}{|t|}$, after some computations, where $\alpha$ is the angle between $r$ and $r'$ at a given t. This angle is not constant since if $t$ is positive then the angle is 0 and if t is negative the angle will be $\pi$.

can anyone confirm or point my possible mistakes. Thanks.

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I suspect that the book intended to write $r(t')$ instead of $r'(t)$. Double check it. – Emanuele Paolini Feb 12 '13 at 9:09