Find the Scalar Tangential and Normal Components of Acceleration of a Particle

Multiple Choice

Find the scalar tangential and normal components of acceleration of a particle with position vector $\mathbf { r } ( t ) = e ^ { t } \{ \cos 6 t , \sin 6 t , 0 \}$

A) $a _ { \mathbf { T } } = \sqrt { 37 } e ^ { t } , a _ { \mathrm { N } } = 6 \sqrt { 37 } e ^ { t }$
B) $a _ { \mathbf { T } } = 6 e ^ { t } , a _ { \mathbf { N } } = 37 e ^ { t }$
C) $a _ { \mathbf { T } } = 6 \sqrt { 37 } e ^ { t } , a _ { \mathrm { N } } = \sqrt { 37 } e ^ { t }$
D) $a _ { \mathbf { T } } = 37 e ^ { t } , a _ { \mathrm { N } } = 6 e ^ { t }$