Find the Principal Unit Normal Vector N for the Curve $r ( t ) = \left( t ^ { 2 } + 4 \right) \mathbf { j } + ( 2 t - 1 ) \mathbf { k }$

question 14

Multiple Choice

Find the principal unit normal vector N for the curve r(t) .
- $r ( t ) = \left( t ^ { 2 } + 4 \right) \mathbf { j } + ( 2 t - 1 ) \mathbf { k }$

• A) \(\mathbf { N } = - \frac { 1 } { \sqrt { \left( t ^ { 2 } + 1 \right) ^ { 3 } } } \mathbf { j } + \frac { t } { \sqrt { \left( t ^ { 2 } + 1 \right) ^ { 3 } } } \mathbf { k }\)
• B) \(\mathbf { N } = \frac { 1 } { \sqrt { \mathrm { t } ^ { 2 } + 1 } } \mathbf { j } - \frac { \mathrm { t } } { \sqrt { \mathrm { t } ^ { 2 } + 1 } } \mathbf { k }\)
• C) \(\mathbf { N } = - \frac { 1 } { \sqrt { t ^ { 2 } + 1 } } \mathbf { j } + \frac { \mathrm { t } } { \sqrt { \mathrm { t } ^ { 2 } + 1 } } \mathbf { k }\)
• D) \(\mathbf { N } = \frac { 1 } { \sqrt { \left( t ^ { 2 } + 1 \right) ^ { 3 } } } \mathbf { j } - \frac { \mathrm { t } } { \sqrt { \left( \mathrm { t } ^ { 2 } + 1 \right) ^ { 3 } } } \mathbf { k }\)

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