Question 1

Find the angle between u and v in radians.
-u = -2i + 8j - 8k, v = 8i + 4j - 5k

Accepted Answer

A)  1.57 
B)  0.50 
C)  1.33 
D)  1.08 
A)  1.57 
B)  0.50 
C)  1.33 
D)  1.08

Question 2

Find the angle between u and v in radians.
-u = -10j and v = 6i - 8k

Accepted Answer

A)  1.67 
B)  0.10 
C)  1.57 
D)  0.00 
A)  1.67 
B)  0.10 
C)  1.57 
D)  0.00

Question 3

Identify the quadric surface by name. Find and describe the xy-, xz-, and yz-traces, when they exist.
-16   - 16   - z = 0

Accepted Answer

A)  Elliptic cone; xz-trace: 16xS1U1P12S1S1P0  - z = 0 (hyperbola); yz-trace: 16yS1U1P12S1S1P0  + z = 0 (hyperbola) 
B)  Elliptic paraboloid; xz-trace: 16xS1U1P12S1S1P0  - z = 0 (hyperbola); yz-trace: 16yS1U1P12S1S1P0  + z = 0 (hyperbola) 
C)  Elliptic paraboloid; xz-trace: 16xS1U1P12S1S1P0  - z = 0 (parabola); yz-trace: 16yS1U1P12S1S1P0  + z = 0 (parabola) 
D)  Hyperbolic paraboloid; xz-trace: 16xS1U1P12S1S1P0  - z = 0 (parabola); yz-trace: 16 yS1U1P12S1S1P0 + z = 0 (parabola) 
A)  Elliptic cone; xz-trace: 16xS1U1P12S1S1P0  - z = 0 (hyperbola); yz-trace: 16yS1U1P12S1S1P0  + z = 0 (hyperbola) 
B)  Elliptic paraboloid; xz-trace: 16xS1U1P12S1S1P0  - z = 0 (hyperbola); yz-trace: 16yS1U1P12S1S1P0  + z = 0 (hyperbola) 
C)  Elliptic paraboloid; xz-trace: 16xS1U1P12S1S1P0  - z = 0 (parabola); yz-trace: 16yS1U1P12S1S1P0  + z = 0 (parabola) 
D)  Hyperbolic paraboloid; xz-trace: 16xS1U1P12S1S1P0  - z = 0 (parabola); yz-trace: 16 yS1U1P12S1S1P0 + z = 0 (parabola)

Question 4

Solve the problem.
-A ramp leading to the entrance of a building is inclined upward at an angle of 6°. A suitcase is to be pulled up the ramp by a handle that makes an angle of 34° with the horizontal. How much force must be applied in the direction of the handle so that the component of the force parallel to the ramp is 50 lbs.?

Accepted Answer

A)  44.15 lbs 
B)  59.98 lbs 
C)  -56.58 lbs 
D)  55.90 lbs 
A)  44.15 lbs 
B)  59.98 lbs 
C)  -56.58 lbs 
D)  55.90 lbs

Question 5

Solve the problem.
-A bullet is fired with a muzzle velocity of 1489 ft/sec from a gun aimed at an angle of 12° above the horizontal. Find the horizontal component of the velocity.

Accepted Answer

A)  309.6 ft/sec 
B)  1256 ft/sec 
C)  1456 ft/sec 
D)  316.5 ft/sec 
A)  309.6 ft/sec 
B)  1256 ft/sec 
C)  1456 ft/sec 
D)  316.5 ft/sec

Question 6

Solve the problem.
-Find the work done by a force of 19i (newtons) in moving an object along a line from the origin to the point   (distance in meters).

Accepted Answer

A)  28.60 joules 
B)  152.0 joules 
C)  228.8 joules 
D)  98.65 joules 
A)  28.60 joules 
B)  152.0 joules 
C)  228.8 joules 
D)  98.65 joules

Question 7

Find the magnitude of u × v and the unit vector parallel to u × v in the direction of u × v.
-u = -   i +   j + k, v = i + j + 2k

Accepted Answer

A)  2   ; -   i +   j -   k 
B)  8;   i -   j -   k 
C)  2   ;   i +   j -   k 
D)  8;   i -   j +   k 
A)  2   ; -   i +   j -   k 
B)  8;   i -   j -   k 
C)  2   ;   i +   j -   k 
D)  8;   i -   j +   k

Question 8

Find v ∙ u.
-v = -3i + 6j and u = 9i + 3j

Accepted Answer

A)  -27i + 18j 
B)  6i + 9j 
C)  -45 
D)  -9 
A)  -27i + 18j 
B)  6i + 9j 
C)  -45 
D)  -9

Question 9

Identify the surface by name.
-x =   +

Accepted Answer

A)  Elliptic paraboloid 
B)  Hyperbolic cylinder 
C)  Hyperbolic paraboloid 
D)  Ellipsoid 
A)  Elliptic paraboloid 
B)  Hyperbolic cylinder 
C)  Hyperbolic paraboloid 
D)  Ellipsoid

Question 10

Find the indicated vector.
-Let u =   . Find -6u.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 11

Express the vector in the form ai + bj + ck.
-  if   is the point ( 3, 6, -4) and   is the point ( 5, 3, -8)

Accepted Answer

A)  v = -2i - 3j + 4k 
B)  v = -2i + 3j + 4k 
C)  v = -2i + 3j - 4k 
D)  v = 2i - 3j - 4k 
A)  v = -2i - 3j + 4k 
B)  v = -2i + 3j + 4k 
C)  v = -2i + 3j - 4k 
D)  v = 2i - 3j - 4k

Question 12

Find v ∙ u.
-v = 3i - 6j and u = -9i + 2j

Accepted Answer

A)  -6i - 4j 
B)  -39 
C)  -27i - 12j 
D)  -15 
A)  -6i - 4j 
B)  -39 
C)  -27i - 12j 
D)  -15

Question 13

Find the indicated vector.
-Let u =   , v =   . Find u + v.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 14

Identify the type of surface represented by the given equation.
-x = -10   , no limit on y

Accepted Answer

A)  Parabolic cylinder 
B)  Hyperboloid of two sheets 
C)  Cylinder 
D)  Sphere 
A)  Parabolic cylinder 
B)  Hyperboloid of two sheets 
C)  Cylinder 
D)  Sphere

Question 15

Match the equation with the surface it defines.    
-  -   =

Accepted Answer

A)  Figure 3 
B)  Figure 2 
C)  Figure 4 
D)  Figure 1 
A)  Figure 3 
B)  Figure 2 
C)  Figure 4 
D)  Figure 1

Question 16

Find the corresponding position vector.
-Define the points P = ( -10, -6) and Q = ( -2, 5). Find the position vector corresponding to   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

Find the intersection.
--2x + 2y = -2, -2y + 5z = 4

Accepted Answer

A)  x = 10t - 1, y = 10t - 2, z = 4t 
B)  x = 10t - 1, y = 10t - 2, z = 4 
C)  x = 10t + 1, y = 10t + 2, z = -4t 
D)  x = 10t - 4, y = 10t + 4, z = 4t 
A)  x = 10t - 1, y = 10t - 2, z = 4t 
B)  x = 10t - 1, y = 10t - 2, z = 4 
C)  x = 10t + 1, y = 10t + 2, z = -4t 
D)  x = 10t - 4, y = 10t + 4, z = 4t

Question 18

Solve the problem.
-For the vectors u and v with magnitudes   = 7 and   = 8, find the angle $\theta$ between u and v which makes   = 5

Accepted Answer

A)  45.58° 
B)  44.42° 
C)  28.96° 
D)  51.32° 
A)  45.58° 
B)  44.42° 
C)  28.96° 
D)  51.32°

Question 19

Match the equation with the surface it defines.    
-  -   -   = 1

Accepted Answer

A)  Figure 1 
B)  Figure 2 
C)  Figure 4 
D)  Figure 3 
A)  Figure 1 
B)  Figure 2 
C)  Figure 4 
D)  Figure 3

Question 20

Find v ∙ u.
-v =   and u =

Accepted Answer

A)    i -   j 
B)  0 
C)    
D)    i -   j 
A)    i -   j 
B)  0 
C)    
D)    i -   j

Find the angle between u and v in radians. -u = -2i + 8j - 8k, v = 8i + 4j - 5k

Find the angle between u and v in radians. -u = -10j and v = 6i - 8k

Identify the quadric surface by name. Find and describe the xy-, xz-, and yz-traces, when they exist. -16 - 16 - z = 0

Solve the problem. -A bullet is fired with a muzzle velocity of 1489 ft/sec from a gun aimed at an angle of 12° above the horizontal. Find the horizontal component of the velocity.

Solve the problem. -Find the work done by a force of 19i (newtons) in moving an object along a line from the origin to the point (distance in meters).

Find the magnitude of u × v and the unit vector parallel to u × v in the direction of u × v. -u = - i + j + k, v = i + j + 2k

Find v ∙ u. -v = -3i + 6j and u = 9i + 3j

Identify the surface by name. -x = +

Find the indicated vector. -Let u = . Find -6u.

Express the vector in the form ai + bj + ck. - if is the point ( 3, 6, -4) and is the point ( 5, 3, -8)

Find v ∙ u. -v = 3i - 6j and u = -9i + 2j

Find the indicated vector. -Let u = , v = . Find u + v.

Identify the type of surface represented by the given equation. -x = -10 , no limit on y

Match the equation with the surface it defines. - - =

Find the corresponding position vector. -Define the points P = ( -10, -6) and Q = ( -2, 5). Find the position vector corresponding to .

Find the intersection. --2x + 2y = -2, -2y + 5z = 4

Match the equation with the surface it defines. - - - = 1

Find v ∙ u. -v = and u =

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Exam 13: Vectors and the Geometry of Space

Find the angle between u and v in radians. -u = -2i + 8j - 8k, v = 8i + 4j - 5k

Find the angle between u and v in radians. -u = -10j and v = 6i - 8k

Identify the quadric surface by name. Find and describe the xy-, xz-, and yz-traces, when they exist. -16 - 16 - z = 0

Solve the problem. -A bullet is fired with a muzzle velocity of 1489 ft/sec from a gun aimed at an angle of 12° above the horizontal. Find the horizontal component of the velocity.

Solve the problem. -Find the work done by a force of 19i (newtons) in moving an object along a line from the origin to the point (distance in meters).

Find the magnitude of u × v and the unit vector parallel to u × v in the direction of u × v. -u = - i + j + k, v = i + j + 2k

Find v ∙ u. -v = -3i + 6j and u = 9i + 3j

Identify the surface by name. -x = +

Find the indicated vector. -Let u = . Find -6u.

Express the vector in the form ai + bj + ck. - if is the point ( 3, 6, -4) and is the point ( 5, 3, -8)

Find v ∙ u. -v = 3i - 6j and u = -9i + 2j

Find the indicated vector. -Let u = , v = . Find u + v.

Identify the type of surface represented by the given equation. -x = -10 , no limit on y

Match the equation with the surface it defines. - - =

Find the corresponding position vector. -Define the points P = ( -10, -6) and Q = ( -2, 5). Find the position vector corresponding to .

Find the intersection. --2x + 2y = -2, -2y + 5z = 4

Solve the problem. -For the vectors u and v with magnitudes = 7 and = 8, find the angle θ\thetaθ between u and v which makes = 5

Match the equation with the surface it defines. - - - = 1

Find v ∙ u. -v = and u =

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters