A portion of the curve \(\mathcal {C}\) traced out by \(\vec {p}(t)\) is shown below. The points associated to \(\vec {p}(t)\) for various \(t\) values are shown on the curve.

Provide the most accurate response to the following questions.

Which of the following vectors is orthogonal to \(\vec {p}(5)?\)

\(\vector {1,0}\) \(\vector {0,1}\) \(\vector {1,1}\) \(\vector {-1,1}\)

Which of the following vectors is parallel to \(\vec {p}'(5)?\)

\(\vector {1,0}\) \(\vector {0,1}\) \(\vector {-1,1}\) \(\vector {1,5}\) \(\vector {1,-5}\) \(\vector {5,1}\) \(\vector {5,-1}\)

Which of the following vectors is parallel to \(\vec {p}'(9)?\)

\(\vector {1,0}\) \(\vector {0,1}\) \(\vector {-1,1}\) \(\vector {1,2}\) \(\vector {1,-2}\) \(\vector {2,1}\) \(\vector {-2,1}\)

Which of the following vectors is parallel to \(\vector {-x(9),y(5)}?\)

\(\vector {1,1}\) \(\vector {1,-1}\) \(\vector {1,2}\) \(\vector {1,-2}\) \(\vector {2,1}\) \(\vector {2,-1}\) more than one of these.