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) \(\mathrm { T } \left( \frac { \pi } { 4 } \right) = \frac { 1 } { 2 } ( \sqrt { 2 } , - \sqrt { 2 } , 0 )\)

Utilize knowledge of specimen handling to maintain specimen integrity.

Identify and manage potential complications or issues in specimen collection and handling.

Understand the correct procedures for blood specimen collection.

Recognize the appropriate actions and considerations in venipuncture.

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Definitions:

Boat Conformation

A specific geometric arrangement of atoms in cyclic molecules resembling a boat, less stable than the chair conformation.

Cyclohexane

A cycloalkane composed of six carbon atoms arranged in a ring, with molecular formula C6H12, used as a solvent and in the manufacture of nylon.

Cis-1-Ethyl-3-Methylcyclohexane

A specific isomer of a six-membered ring compound with ethyl and methyl substituents in a cis configuration.

Stable Conformation

The most energetically favorable arrangement of atoms in a molecule that minimizes strain.