Find a Vector-Valued Function, Using the Given Parameter, to Represent $\begin{array}{ll}\text { Surfaces } & \text { Parameter } \\x^{2}+y^{2}=25, z=x^{2} & x=5 \sin 2 \pi t\end{array}$

question 26

Multiple Choice

Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. $\begin{array}{ll}\text { Surfaces } & \text { Parameter } \\x^{2}+y^{2}=25, z=x^{2} & x=5 \sin 2 \pi t\end{array}$

• A) \(\mathbf { r } ( t ) = 25 \sin 2 \pi t \mathbf { i } + 25 \cos 2 \pi t \mathbf { j } - 5 \sin ^ { 2 } 2 \pi t \mathbf { k }\)
• B) \(\mathbf { r } ( t ) = 5 \sin 2 \pi t \mathbf { j } + 5 \cos 2 \pi t \mathbf { i } + 25 \sin ^ { 2 } 2 \pi \mathbf { k }\)
• C) \(\mathbf { r } ( t ) = 5 \sin 2 \pi t \mathbf { i } + 5 \cos 2 \pi t \mathbf { j } - 25 \sin ^ { 2 } 2 \pi \mathbf { k }\)
• D) \(\mathbf { r } ( t ) = 5 \sin 2 \pi t \mathbf { i } + 5 \cos 2 \pi t \mathbf { j } + 25 \sin ^ { 2 } 2 \pi t \mathbf { k }\)
• E) \(\mathbf { r } ( t ) = 25 \sin 2 \pi \mathbf { i } + 25 \cos 2 \pi t \mathbf { j } + 5 \sin ^ { 2 } 2 \pi t \mathbf { k }\)

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