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 10 Worth 8 points Evaluate the surface integral

Question 2 Worth 8 points Use spherical coordinates to set up the integral 

Question 2 Worth 8 points Find the equation of the plane that passes through the points  and

Question 1 Worth 10 points Given vectors  and

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

Question 4 Worth 8 points Find the equation of the normal line to the surface     at the point .  

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 unit tangent vector when for the curve defined by .

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

Question 5 Worth 8 points Find the distance between the planes