Vector functions basic question

Question

While evaluating a single variable three component vector function at point $c$, can we also call the three components of the result as three outputs of our function at point $c$?

Answer 1

Yes that is correct.

Your function is defined as $$F(t)=<f(t), g(t), h(t)>$$ where $f(t), g(t), h(t)$ are real valued functions. You may express your function as parametric $$x=f(t), y=g(t), z=h(t)$$

These component functions are the out put where $t$ is the input of the vector function $F(t)$

For example for a spiral you may have $$x=\sin t, y=\cos t, z=t$$ or $$ S(t) = <\sin t, \cos t, t>$$