Let $\mathbf { r } ( t ) = \cos ( 2 t ) \mathbf { i } + \sin ( 2 t ) \mathbf { j } + 3 t \mathbf { k }$ Then the unit normal vector $\mathbf { n } \left( \frac { \pi } { 4 } \right)$ is

A)i
B) $- \frac { 1 } { \sqrt { 5 } } \mathbf { i } + \frac { 4 } { \sqrt { 5 } } \mathbf { k }$
C) $\frac { 2 } { \sqrt { 29 } } \mathbf { j } + \frac { 5 } { \sqrt { 29 } } \mathbf { k }$
D) $- \mathbf { j }$
E)k

Question

Let $\mathbf { r } ( t ) = \cos ( 2 t ) \mathbf { i } + \sin ( 2 t ) \mathbf { j } + 3 t \mathbf { k }$ Then the unit normal vector $\mathbf { n } \left( \frac { \pi } { 4 } \right)$ is

A)i
B) $- \frac { 1 } { \sqrt { 5 } } \mathbf { i } + \frac { 4 } { \sqrt { 5 } } \mathbf { k }$
C) $\frac { 2 } { \sqrt { 29 } } \mathbf { j } + \frac { 5 } { \sqrt { 29 } } \mathbf { k }$
D) $- \mathbf { j }$
E)k

Quizplus · Accepted Answer

The Answer of Let $\mathbf { r } ( t ) = \cos ( 2 t ) \mathbf { i } + \sin ( 2 t ) \mathbf { j } + 3 t \mathbf { k }$ Then the unit normal vector $\mathbf { n } \left( \frac { \pi } { 4 } \right)$ is

A)i
B) $- \frac { 1 } { \sqrt { 5 } } \mathbf { i } + \frac { 4 } { \sqrt { 5 } } \mathbf { k }$
C) $\frac { 2 } { \sqrt { 29 } } \mathbf { j } + \frac { 5 } { \sqrt { 29 } } \mathbf { k }$
D) $- \mathbf { j }$
E)k

Let r(t)=cos⁡(2t)i+sin⁡(2t)j+3tk\mathbf { r } ( t ) = \cos ( 2 t ) \mathbf { i } + \sin ( 2 t ) \mathbf { j } + 3 t \mathbf { k }r(t)=cos(2t)i+sin(2t)j+3tk

Let $\mathbf { r } ( t ) = \cos ( 2 t ) \mathbf { i } + \sin ( 2 t ) \mathbf { j } + 3 t \mathbf { k }$