For the Curve R(t), Find an Equation for the Indicated

Multiple Choice

For the curve r(t) , find an equation for the indicated plane at the given value of t.
- $\left. \mathbf { r } ( \mathrm { t } ) = \left( 3 \sin \frac { 5 } { 3 } \mathrm { t } + 7 \right) \mathbf { i } + ( 3 \cos 20 \mathrm { t } ) - 6 \right) \mathbf { j } + 12 \mathrm { k } \mathbf { k }$ ; osculating plane at $t = 2.5 \pi$ .

A) $\frac { 12 } { 169 } ( y - 6 ) + \frac { 60 } { 169 } ( z - 30 \pi ) = 0$
B) $\frac { 12 } { 13 } ( y + 6 ) + \frac { 60 } { 13 } ( z + 30 ) = 0$
C) $\frac { 12 } { 13 } ( y + 6 ) + \frac { 60 } { 13 } ( z - 30 \pi ) = 0$
D) $\frac { 12 } { 13 } ( x - 7 ) + \frac { 60 } { 13 } ( z - 30 \pi ) = 0$