Find the Principle Unit Normal Vector to the Curve Given $$\mathbf { r } ( t ) = t \mathbf { i } + \frac { 4 } { t } \mathbf { j } , \quad t = 3$$

question 7

Multiple Choice

Find the principle unit normal vector to the curve given below at the specified point. $$\mathbf { r } ( t ) = t \mathbf { i } + \frac { 4 } { t } \mathbf { j } , \quad t = 3$$

• A) \(N ( 3 ) = \frac { 4 } { \sqrt { 97 } } \mathbf { i } - \frac { 9 } { \sqrt { 97 } } \mathbf { j }\)
• B) \(N ( 3 ) = \frac { 4 } { \sqrt { 97 } } \mathbf { i } + \frac { 9 } { \sqrt { 97 } } \mathbf { j }\)
• C) \(N ( 3 ) = \frac { 4 } { \sqrt { 1297 } } \mathbf { i } - \frac { 9 } { \sqrt { 1297 } } \mathbf { j }\)
• D) \(N ( 3 ) = \frac { 4 } { \sqrt { 1297 } } \mathbf { i } + \frac { 9 } { \sqrt { 1297 } } \mathbf { j }\)
• E) \(N ( 3 ) = \frac { - 4 } { \sqrt { 97 } } \mathbf { i } - \frac { 9 } { \sqrt { 97 } } \mathbf { j }\)

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Definitions:

Deconstructed Self-concept

Refers to the process of breaking down one's self-identity into various components to better understand the influences and factors that shape their sense of self.

Selective Perception

The process by which individuals selectively interpret what they see, hear, and feel based on their own experiences, attitudes, and beliefs.

Selective Retention

The process by which individuals remember only information that supports their beliefs or opinions, often ignoring opposing evidence.

Stimulus Discrimination

Stimulus discrimination is a concept in behavioral psychology where an organism learns to respond differently to various stimuli that are similar but not identical.