1. Which of the following is an equation of the plane tangent to the surface x^{2} + y^{2}  3z = 2 at the point (2, 4, 6) ?
A. x +y +z 2 = 0 
B. 2x 4y +6z = 0 
C. 2x 4y +6z 2 = 0 
D. 4x +8y +3z = 0 
E. 4x +8y +3z +22 = 0 
2. Let C be the curve in R^{3} defined by the parametric equations
x(t) = cos(e^{t})
y(t) = sin(e^{t})
z(t) = e^{t}
for t in [0,2]. What is the length of C?
A. 
B. 
C. 
D. 
E. 
3. Which of the following is an equation of the normal line
to the graph of
y^{2} + 6y  x = 4 at the point (3,1)?
A. 8x  y = 23 
B. x + 8y = 11 
C. x  8y = 5 
D. 8x + y = 25 
E. 8x + y = 25 
4. Which of the following is an equation of the tangent plane to the surface
z = x^{2} + y^{2}x  2 at the point (1,1,0)?
A. 3x + 2y + z = 5 
B. 3x + 2y  z = 5 
C. 3x + 2y  z = 4 
D. 2x + 2y z = 4 
E. 2x + 2y + z = 4 
5. Which of the following is an equation of the line normal to y = e^{x} at (1,e)?
A. y = e + e^{1}  e^{1}x 
B. y = e  e^{1} + e^{1}x 
C. y = ex 
D. y = 2e  ex 
E. y = 2e + ex 
6. Which of the following is an equation of the plane tangent to the surface xyz^{2} = 1 at the point (1,1,1)?
A. x + y  2z = 4 
B. x + y + z = 1 
C. x + y  z = 3 
D. x + y + 2z = 0 
E. x + y  2z = 3 
7. The equations below define a line L in R^{3}
x + y = 1
x + z = 1
Which of the following equations defines a plane that is perpendicular to L?
A. x + y = 1 
B. x + z = 1 
C. y  z = 0 
D. 2x + y + z = 2 
E. x  y  z = 0 
8. The coordinates of an object moving in R^{3} at time t are x = t, y = t^{2}, z = (2/3)t^{3}. What is the distance traveled by the object between t = 0 and t = 3 ?
A. 21 
B. 27 
C. 57 
D. 75 
E. 3(46)^{1/2} 
9. Let T be the closed region in the first quadrant of the xyplane bounded by x = 0, x = 1, y = x, and y = x^{3} + 1. What is
A. 14/3 
B. 52/9 
C. 56/9 
D. 20/3 
E. 172/9 
10. What is the cosine of the angle between the vectors
A. 3/4 
B. 1/150 
C. 3^{1/2}/15 
D. 1/2 
E. 2 
11. The position vector to a curve in R^{3} is given by
What is the unit tangent vector at t = Pi/3 ?
A. 
B. 
C. 
D. 
E. 
12. Let,
Which of the following is a unit normal vector to S at t = Pi/6 ?
A. 
B. 
C. 
D. 
E. 
13. Let S be the closed region in the xyplane whose boundary is the parallelogram with vertices (0,0), (2,0), (3,1), and (1,1).
A. 8 
B. 28/3 
C. 32/3 
D. 73/6 
E. 15 
14. The coordinates of an object moving through R^{3} are
for time t > 0, where a, b, and c are constants. What is the speed of the object at time t?
A. 
B.

C. 
D. 
E. 
15. What is the magnitude of the projection of the vector <1,2,3> onto the vector <4,3,2> ?
A. (14)^{1/2}/16 
B. 16/(406)^{1/2} 
C. 16/(29)^{1/2} 
D. 16/(14)^{1/2} 
E. 16 
16. What is the volume of the closed region in R^{3} bounded by z = 9  x^{2}  y^{2} and z = 0 ?
A. 
B. 
C. 
D. 
E. 
17. What is an equation of the plane tangent to the surface
at the point (6,3,1) ?
A. 2x + 6y  z = 5 
B. 2x + 6y  z = 5 
C. x + y + z = 2 
D. x + y  z = 4 
E. z = 1 
18. The line normal to the surface 3x + y^{2}  z^{2} = 0 at the point (3,0,3) also intersects the surface at what other point?
A. (3/4,0,21/2) 
B. (0,0,0) 
C. (3,0,3) 
D. (21/4,0,3/2) 
E. (27/4,0,9/2) 
19. What is the cosine of the angle between the vectors <2,1,2> and <6,3,2> in R^{3} ?
A. 13/10 
B. 10/13 
C. 13/21 
D. 3/7 
E. 19/21 