Final answer:
The question is about finding the plane equation for a curve defined by a vector function. It involves calculating the cross product of two tangent vectors on the curve, determined by the derivative of the vector function at different values of the parameter t.
Step-by-step explanation:
The student's question is about finding an equation of the plane that contains a curve represented by the vector equation r(t) = (5t, sin(t), t⁴). To find the equation of a plane, we would generally need a point on the plane and the normal vector to the plane. However, as the curve is represented by a parametric equation, we should first find two distinct directions vectors on the curve by taking the derivative of r(t) to find the tangent vector r'(t) at two different values of t. With two tangent vectors, we can find the normal vector to the plane by taking their cross product. Unfortunately, the information provided does not directly help us with solving for the plane equation as it appears to be more related to mechanics and angular velocity problems.