Find a Vector Function That Represents the Curve of Intersection $x ^ { 2 } + 7 y ^ { 2 } + 7 z ^ { 2 } = 49$

question 14

Multiple Choice

Find a vector function that represents the curve of intersection of the two surfaces: the top half of the ellipsoid $x ^ { 2 } + 7 y ^ { 2 } + 7 z ^ { 2 } = 49$ and the parabolic cylinder $y = x ^ { 2 }$ .

• A) \(\mathbf { r } ( t ) = t \mathbf { i } + t ^ { 4 } \mathbf { j } + \sqrt { \frac { 49 - t ^ { 2 } + 7 t } { 7 } } \mathbf { k }\)
• B) \(\mathbf { r } ( t ) = t \mathbf { i } + t ^ { 2 } \mathbf { j } + \sqrt { \frac { 49 + t ^ { 2 } - 7 t ^ { 4 } } { 7 } } \mathbf { k }\)
• C) \(r ( t ) = t \mathbf { i } + t ^ { 2 } \mathbf { j } + \sqrt { \frac { 49 - t ^ { 2 } - 7 t } { 7 } } \mathbf { k }\)
• D) \(\mathbf { r } ( t ) = t \mathbf { i } + t ^ { 2 } \mathbf { j } + \sqrt { \frac { 7 - t ^ { 2 } - 7 t ^ { 4 } } { 7 } } \mathbf { k }\)
• E) \(\mathbf { r } ( t ) = t \mathbf { i } - t ^ { 2 } \mathbf { j } - \sqrt { \frac { 49 - t ^ { 2 } - 7 t } { 7 } } \mathbf { k }\)

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