Reparametrize the Curve with Respect to Arc Length Measured from the Point

question 1

Multiple Choice

Reparametrize the curve with respect to arc length measured from the point where $t = 0$ in the direction of increasing $t$ .
$\mathbf { r } ( t ) = ( 7 + 3 t ) \mathbf { i } + ( 10 + 9 t ) \mathbf { j } - ( 6 t ) \mathbf { k }$

• A) \(\mathbf { r } ( t ( s ) ) = \left( 7 - \frac { 3 } { \sqrt { 126 } } s \right) \mathbf { i } + \left( 10 + \frac { 9 } { \sqrt { 126 } } s \right) \mathbf { j } - \left( \frac { 6 s } { \sqrt { 126 } } \right) \mathbf { k }\)
• B) \(\mathbf { r } ( t ( s ) ) = \left( 7 + \frac { 3 } { \sqrt { 126 } } s \right) \mathbf { i } + \left( 10 - \frac { 9 } { \sqrt { 126 } } s \right) \mathbf { j } - \left( \frac { 6 s } { \sqrt { 126 } } \right) \mathbf { k }\)
• C) \(\mathbf { r } ( t ( s ) ) = \left( 7 + \frac { 3 } { \sqrt { 126 } } s \right) \mathbf { i } + \left( 10 + \frac { 9 } { \sqrt { 126 } } s \right) \mathbf { j } - \left( \frac { 6 s } { \sqrt { 126 } } \right) \mathbf { k }\)
• D)
• \(\mathbf { r } ( t ( s ) ) = \left( 7 + \frac { 3 } { \sqrt { 126 } } s \right) \mathbf { i } + \left( 10 + \frac { 9 } { \sqrt { 126 } } s \right) \mathbf { j } + ( 6 s ) \mathbf { k }\)
• E)
• \(\mathbf { r } ( t ( s ) ) = \left( 7 + \frac { 3 } { \sqrt { 126 } } s \right) \mathbf { i } + \left( 10 + \frac { 9 } { \sqrt { 126 } } s \right) \mathbf { j } - ( 6 s ) \mathbf { k }\)

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Definitions:

Output Device

A hardware component used to convey information from a computer or system to the external environment, such as a monitor, speaker, or printer.

Input Device

Any device that is used to feed data or control signals into a computer or processing system, such as a keyboard, mouse, or sensor.

IREF

IREF often stands for reference current, a specific, stable current used as a reference point in electronic circuits for biasing and stabilizing purposes.

Internal Reference

A predetermined or fixed point within a system used as a standard for measurement or comparison.