Find the Principle Unit Normal Vector to the Curve Given $\mathbf { r } ( t ) = 5 \cos t \mathbf { i } + 5 \sin t \mathbf { j } , \quad t = \frac { 5 \pi } { 3 }$

Multiple Choice

Find the principle unit normal vector to the curve given below at the specified point. $\mathbf { r } ( t ) = 5 \cos t \mathbf { i } + 5 \sin t \mathbf { j } , \quad t = \frac { 5 \pi } { 3 }$

A) $\mathbf { N } = \left( \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right\}$
B) $\mathbf { N } = \left( \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$
C) $\mathbf { N } = \left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$
D) $\mathbf { N } = \left( - \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$
E) $\mathrm { N } = \left( - \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$