Answer:
The function a (t) is a vector function composed of the component functions [tex]a_ {1} (t) = cost, a_ {2} (t) = sin2t[/tex] and [tex]a_ {3} (t) = cos2t[/tex]. How [tex]a_ {1} (t), a_ {2} (t), a_ {3} (t)[/tex] are infinitely derivable functions in R, so they are regular functions in R.
Now, for[tex]t = 0[/tex], you have to [tex]a (0) = (cos (0), sin2 (0), cos2 (0)) = (1, 0, 1)[/tex]. How the functions [tex]a_ {1} (t), a_ {2} (t), a_ {3} (t)[/tex] are periodic functions with period [tex]2 \pi,[/tex] the vector function [tex]a (t)[/tex] will take the same point [tex](1, 0 , 1)[/tex] at [tex]t = 2n\pi, n = 0, 1, 2, 3, ...[/tex] then the vector function is auto-intercepted
Step-by-step explanation:
