Find the Unit Tangent Vector of the Given Curve $$r ( t ) = 3 t ^ { 5 } i - 12 t ^ { 5 } j + 4 t ^ { 5 } \mathbf { k }$$

question 70

Multiple Choice

Find the unit tangent vector of the given curve.
- $$r ( t ) = 3 t ^ { 5 } i - 12 t ^ { 5 } j + 4 t ^ { 5 } \mathbf { k }$$

• A) \(\mathrm { T } = \frac { 3 } { 13 } \mathrm { i } + \frac { 12 } { 13 } \mathrm { j } + \frac { 4 } { 13 } \mathbf { k }\)
• B) \(T = \frac { 3 } { 13 } \mathbf { i } - \frac { 12 } { 13 } j \mathbf { j } - \frac { 4 } { 13 } \mathbf { k }\)
• C) \(\mathbf { T } = \frac { 3 } { 169 } \mathbf { i } - \frac { 12 } { 169 } \mathbf { j } + \frac { 4 } { 169 } \mathbf { k }\)
• D) \(\mathbf { T } = \frac { 3 } { 13 } \mathbf { i } - \frac { 12 } { 13 } \mathbf { j } + \frac { 4 } { 13 } \mathbf { k }\)

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