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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Definitions:

Sublimation

A defense mechanism in psychology where unacceptable impulses or urges are transformed into more socially acceptable actions or behaviors.

Defense Mechanism

Psychological strategies employed unconsciously to protect the self from anxiety, social sanctions, or to provide a refuge from a situation with which one cannot currently cope.

Oedipus Complex

A psychoanalytic theory by Freud, referring to a child's feelings of desire for the opposite-sex parent and jealousy towards the same-sex parent.

Phallic Complex

The phallic complex is a concept in psychoanalytic theory referring to a stage of psychosexual development where children's interest and attachment are focused on their genitalia and the differences between sexes.