Find the Principle Unit Normal Vector to the Curve Given $$\mathbf { r } ( t ) = t \mathbf { i } + 4 t ^ { 2 } \mathbf { j } , \quad t = 3$$

question 82

Multiple Choice

Find the principle unit normal vector to the curve given below at the specified point. $$\mathbf { r } ( t ) = t \mathbf { i } + 4 t ^ { 2 } \mathbf { j } , \quad t = 3$$

• A) \(N ( 3 ) = \frac { - 24 } { \sqrt { 145 } } \mathbf { i } - \frac { 1 } { \sqrt { 145 } } \mathbf { j }\)
• B) \(N ( 3 ) = \frac { - 24 } { \sqrt { 145 } } \mathbf { i } + \frac { 1 } { \sqrt { 145 } } \mathbf { j }\)
• C) \(N ( 3 ) = \frac { - 24 } { \sqrt { 577 } } \mathbf { i } - \frac { 1 } { \sqrt { 577 } } \mathbf { j }\)
• D) \(N ( 3 ) = \frac { - 24 } { \sqrt { 577 } } \mathbf { i } + \frac { 1 } { \sqrt { 577 } } \mathbf { j }\)
• E) \(N ( 3 ) = \frac { 24 } { \sqrt { 577 } } \mathbf { i } - \frac { 1 } { \sqrt { 577 } } \mathbf { j }\)

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