Find the Unit Normal Vector N(t) to the Curve R $\left\langle t , 2 t , t ^ { 2 } \right\rangle$

question 20

Multiple Choice

Find the unit normal vector N(t) to the curve r (t) = $\left\langle t , 2 t , t ^ { 2 } \right\rangle$ when t = 1.

• A) \(\left\langle \frac { 1 } { 3 } , \frac { 2 } { 3 } , \frac { 2 } { 3 } \right\rangle\)
• B) \(( 1,0,0 )\)
• C)\(( 0,1,0)\)
• D) \(\left( 0 , \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } \right)\)
• E) \(\left( - \frac { 2 } { 3 \sqrt { 5 } } , - \frac { 4 } { 3 \sqrt { 5 } } , \frac { 5 } { 3 \sqrt { 5 } } \right)\)
• F) \(\left( \frac { 1 } { \sqrt { 2 } } , 0 , \frac { 1 } { \sqrt { 2 } } \right)\)
• G) \(\left( \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } , 0 \right)\)
• H) \(\left( \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } \right)\)

---

Definitions:

Phototropin

A protein that acts as a blue-light receptor, causing phototropic responses in plants towards light sources.

Phototropic Response

the growth or movement of a plant organ toward or away from light, as a response to its direction.

Phytochrome

A blue-green, proteinaceous pigment involved in a wide variety of physiological responses to light; occurs in two interconvertible forms, Pr (red-absorbing phytochrome) and Pfr (far-red-absorbing phytochrome).

Bolting

The production of a tall flower stalk by a plant that grows vegetatively as a rosette (growth habit with a short stem and a circular cluster of leaves).