Suppose the vector-valued function r(t) = (f(t), g(t), h(t)) is smooth on an interval containing the point t₀. The line tangent to r(t) at t = t₀ is the line parallel to the tangent vector r'(t₀) that passes through (f(t₀), g(t₀), h(t₀)). For each of the following functions, find an equation of the line tangent to the curve at t = t₀. Choose an orientation for the line that is the same as the direction of r'.

r(t) = (e^t, e^2t, e^3t); t₀ = 0