Find the Unit Tangent Vector of the Given Curve $$r ( t ) = ( 2 \cos 6 t ) i + ( 2 \sin 6 t ) j - 5 t k$$

question 49

Multiple Choice

Find the unit tangent vector of the given curve.
- $$r ( t ) = ( 2 \cos 6 t ) i + ( 2 \sin 6 t ) j - 5 t k$$

• A) \(\mathbf { T } = \left( - \frac { 12 } { 13 } \sin 6 \mathrm { t } \right) \mathbf { i } + \left( \frac { 12 } { 13 } \cos 6 \mathrm { t } \right) \mathbf { j } - \frac { 5 } { 13 } \mathbf { k }\)
• B) \(T = \left( - \frac { 12 } { 13 } \cos 6 t \right) i + \left( \frac { 12 } { 13 } \sin 6 t \right) j - \frac { 5 } { 13 } \mathbf { k }\)
• C) \(\mathrm { T } = \left( - \frac { 12 } { 169 } \cos 6 \mathrm { t } \right) \mathrm { i } + \left( \frac { 12 } { 169 } \sin 6 \mathrm { t } \right) \mathrm { j } - \frac { 5 } { 169 } \mathbf { k }\)
• D) \(T = \left( - \frac { 2 } { 13 } \sin 6 t \right) i + \left( \frac { 2 } { 13 } \cos 6 t \right) j - \frac { 5 } { 13 } \mathbf { k }\)

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