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.
- $\mathbf { r } ( \mathrm { t } ) = ( \mathrm { t } + 6 ) \mathbf { i } + ( \ln ( \cos \mathrm { t } ) - 8 ) \mathbf { j } + 7 \mathbf { k } , - \pi / 2 < \mathrm { t } < \pi \cdot 2 ;$ rectifying plane $\mathrm { at } \mathrm {} \mathrm { t } = \frac { \pi } { 4 }$ .

A) $\frac { \sqrt { 2 } } { 2 } \left( x - \left( \frac { \pi } { 4 } + 6 \right) \right) - \frac { \sqrt { 2 } } { 2 } \left( y - \left( \ln \left( \frac { \sqrt { 2 } } { 2 } \right) - 8 \right) \right) = 0$
B) $- \frac { \sqrt { 2 } } { 2 } \left( x - \left( \frac { \pi } { 4 } + 6 \right) \right) + \frac { \sqrt { 2 } } { 2 } \left( y - \left( \ln \left( \frac { \sqrt { 2 } } { 2 } \right) - 8 \right) \right) = 0$
C) $\frac { \sqrt { 2 } } { 2 } ( x - ( 1 + 6 ) ) = 0$
D) $\left. \frac { \sqrt { 2 } } { 2 } \left( x - \left( \frac { \pi } { 4 } + 6 \right) \right) \right) ^ { \prime } + \frac { \sqrt { 2 } } { 2 } \left( y - \left( \ln \left( \frac { \sqrt { 2 } } { 2 } \right) - 8 \right) \right) = 0$