Question 4 Worth 8 points Find a set of parametric equations of the line that passes through the point

Question 6 Worth 8 points Find the work done by a force  that moves an object from the point  to the point  along a straight line. The distance is measured in meters and the force in newtons.

Question 2 Worth 8 points Find the equation of the plane through the point with normal vector

Question 8 Worth 8 points Evaluate the integral 

Question 9 Worth 8 points Use Lagrange multipliers to find the maximum and minimum values of the function     subject to the constraint     .

Question 5 Worth 8 points Find the work done by the force field on a particle that moves along the curve where  in moving an object along an arch of the cycloid

Question 10 Worth 8 points Find the length of the curve where , and

Question 6 Worth 8 points Find the velocity, acceleration, and speed of an object with position function for    .

Question 12 Worth 10 points a.    Sketch the plane curve   and the vectors and when .    (Do NOT attempt to find  and  when making this sketch, and note that this a 2-dimensional sketch).   b.    Find the scalar tangential component of acceleration   of a particle with position vector .

Question 11 Worth 8 points Find the position and velocity vectors of a particle that has the given acceleration and the given initial velocity and position: ,  , and  .