Find the Principle Unit Normal Vector to the Curve Given $$\mathbf { r } ( t ) = t \mathbf { i } + 4 t ^ { 2 } \mathbf { j } , \quad t = 3$$

question 82

Multiple Choice

Find the principle unit normal vector to the curve given below at the specified point. $$\mathbf { r } ( t ) = t \mathbf { i } + 4 t ^ { 2 } \mathbf { j } , \quad t = 3$$

• A) \(N ( 3 ) = \frac { - 24 } { \sqrt { 145 } } \mathbf { i } - \frac { 1 } { \sqrt { 145 } } \mathbf { j }\)
• B) \(N ( 3 ) = \frac { - 24 } { \sqrt { 145 } } \mathbf { i } + \frac { 1 } { \sqrt { 145 } } \mathbf { j }\)
• C) \(N ( 3 ) = \frac { - 24 } { \sqrt { 577 } } \mathbf { i } - \frac { 1 } { \sqrt { 577 } } \mathbf { j }\)
• D) \(N ( 3 ) = \frac { - 24 } { \sqrt { 577 } } \mathbf { i } + \frac { 1 } { \sqrt { 577 } } \mathbf { j }\)
• E) \(N ( 3 ) = \frac { 24 } { \sqrt { 577 } } \mathbf { i } - \frac { 1 } { \sqrt { 577 } } \mathbf { j }\)

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Definitions:

SPSS

Statistical Package for the Social Sciences, a software package used for data management and statistical analysis.

T Test

A statistical test used to compare the means of two groups and determine if they are significantly different from each other.

T Statistic

A type of statistic used in hypothesis testing, especially for small sample sizes, calculated to compare an observed sample mean to a theoretical population mean.

Straight-line Relationship

A linear connection between two variables, represented graphically by a straight line, indicating a constant rate of change.