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

question 40

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 $\mathbf { N } ( t )$ be the unit tangent vector and unit normal vector to $C$ corresponding to $t$ . The plane determined by $\mathbf { T }$ and $\mathbf { N }$ 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) \(x = 2\)

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