To the nearest degree, find the angle between the vectors: v = -i + 3j + [a]k w = 2i + [b]j + 4k

Match the equation with the surface it defines. identify the surface by type (paraboloid, ellipsoid, etc.) Equation:    3×2 + 3y2 + 10z2 = 50 Which graph? [1] Choice A Choice B Choice C   What is the name of the graph?  [2]

Match the equation with the surface it defines. identify the surface by type (paraboloid, ellipsoid, etc.) Equation:    3×2 + 3y2 + 3z2 = 36 Which graph? [1] Choice A Choice B Choice C   What is the name of the graph?  [2]

Write the equation of the line that is normal to the plane x – 3y + 4z = 19 and passes through the point (6, -2, 3). 

Write the equation of the line that is normal to the plane 4x – y + 3z = 19 and passes through the point (5, 3, -1). 

Write the equation of the plane that contains the points P(0, 0, 0), Q(1, 2, 3), and R(2, 1, [a]).  Write your final answer in the form ax + by + cz = d.     

If an converges to 0, then 

Part Four: Material from Exam #4 For multiple choice, T/F, and fill in the blank questions, please answer accordingly. For free response, please work your problem on your scratch paper. 

Part One: Material from Exam #1 For multiple choice, T/F, and fill in the blank questions, please answer accordingly. For free response, please work your problem on your scratch paper.     

If an does not converge to 0, then