Find the Unit Tangent Vector $\mathrm { T } ( t ) \text { for the line tangent to the space curve }$

question 59

Multiple Choice

Find the unit tangent vector
$\mathrm { T } ( t ) \text { for the line tangent to the space curve }$ $\mathbf { r } ( t ) = \langle 12 \cos t , 12 \sin t , 3 )$ at point $p ( 6 \sqrt { 2 } , 6 \sqrt { 2 } , 3 )$ .

• A) \(\mathbf { T } \left( \frac { \pi } { 4 } \right) = \frac { 1 } { 4 } ( - \sqrt { 2 } , - \sqrt { 2 } , 3 )\)
• B) \(\mathrm { T } \left( \frac { \pi } { 4 } \right) = \frac { 1 } { 4 } ( - \sqrt { 2 } , \sqrt { 2 } , 0 )\)
• C) \(\mathrm { T } \left( \frac { \pi } { 4 } \right) = \frac { 1 } { 2 } ( \sqrt { 2 } , - \sqrt { 2 } , 3 )\)
• D) \(\mathrm { T } \left( \frac { \pi } { 4 } \right) = \frac { 1 } { 2 } ( - \sqrt { 2 } , \sqrt { 2 } , 0 )\)
• E) \(\mathrm { T } \left( \frac { \pi } { 4 } \right) = \frac { 1 } { 2 } ( \sqrt { 2 } , - \sqrt { 2 } , 0 )\)

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