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:

Sertoli Cells

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Semen

A fluid containing spermatozoa and secretions from the male reproductive glands, involved in the fertilization process.

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A type of cell division in sexually reproducing organisms that results in four daughter cells, each with half the chromosome number of the parent cell.

Vas Deferens

The duct that conveys sperm from the testicle to the urethra.