Let C Be a Smooth Curve Defined By $\mathbf { r } ( t ) = 2 \mathbf { i } + 3 t \mathbf { j } + 2 t ^ { 2 } \mathbf { k }$

Multiple Choice

Let C be a smooth curve defined by $\mathbf { r } ( t ) = 2 \mathbf { i } + 3 t \mathbf { j } + 2 t ^ { 2 } \mathbf { k }$ , and let $\mathbf { T } ( t )$ and $\mathrm { N } ( t )$ be the unit tangent vector and unit normal vector to C corresponding to t. The plane determined by T and N is called the osculating plane. Find an equation of the osculating plane of the curve described by $\mathbf { r } ( t )$ at $t = 1$

A) $z = 2$
B) $y = 3$
C) $2 x + 3 y + 2 z = 1$
D) $x = 2$