6. (18 points) Consider the vector function r(t) = ( eat,

6. (18 points) Consider the vector fimction r(t) ( e2t, sin(Tt) ). (a) Find the domain of the vector function. (b) Find the tangent vecto to the space curve at the point where t = 0. (c) Find the vector and parametric equations for the tangent line to the parametrize curve at the point (e2, 1, O).