a. Sketch the plane curve with the given vector equation. b. Find r' (t). c. Sketch the position vector r (t) and the tangent vector r' (t) for the given value of t. r (t) = (cost + 1) i+ (sint - 1) j, t=-7/3 Find the derivative of the vector function. r (t) = t sin ti+ et cost j + sint cost k If r (t) # 0, show that d dt |r (t) = Ir (t)| r (t) . I' (t) W [Hint: |r (t) |2 = r(t) . r(t) ]