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 1 If r (t) # 0, show that d dt I (t) | = r (t) . I' (t) W |r (t)| [Hint: |r (t) |2 = 1(t) . I (t) ]

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