Question 1

The equation for the cylinder with radius 4 oriented symmetric about the z-axis is

Accepted Answer

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

Question 2

Identify the trace of the surface defined by   when   .

Accepted Answer

A)  Circle 
B)  Ellipse 
C)  Parabola 
D)  Hyperbola 
E)  Line 
A)  Circle 
B)  Ellipse 
C)  Parabola 
D)  Hyperbola 
E)  Line

Question 3

Find

Accepted Answer

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

Question 4

If   ,   , and   , find   and   .

Accepted Answer

The answer of If   ,   ,...

Question 5

Identify the trace of the surface defined by   when   .

Accepted Answer

A)  Circle 
B)  Ellipse 
C)  Parabola 
D)  Hyperbola 
E)  Line 
A)  Circle 
B)  Ellipse 
C)  Parabola 
D)  Hyperbola 
E)  Line

Question 6

Convert   from cylindrical to spherical coordinates.

Accepted Answer

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

Question 7

What are the components of v.   ?

Accepted Answer

A)  0 and 0 
B)  -9 and -8 
C)  -8 and 10 
D)  1, -9, and -8 
E)    and 0 
A)  0 and 0 
B)  -9 and -8 
C)  -8 and 10 
D)  1, -9, and -8 
E)    and 0

Question 8

Let   . Find the vector in the same direction as u with twice the length of u.

Accepted Answer

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

Question 9

At what point does the line   intersect the plane containing the point (0, -1, 0) which is parallel to the xz- plane?

Accepted Answer

A)  (8, 0, 5) 
B)  (8, -1, 5) 
C)  (8, 1, 1) 
D)  (6, 6, 5) 
E)  (2, 5, 1) 
A)  (8, 0, 5) 
B)  (8, -1, 5) 
C)  (8, 1, 1) 
D)  (6, 6, 5) 
E)  (2, 5, 1)

Question 10

If   , find

Accepted Answer

A)  114 
B)  -114 
C)  162 
D)  -162 
E)  0 
A)  114 
B)  -114 
C)  162 
D)  -162 
E)  0

Question 11

Let   . Find the vector x that satisfies   .

Accepted Answer

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

Question 12

Find the angle between   and   .

Accepted Answer

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

Question 13

Identify the trace of the surface defined by   when   .

Accepted Answer

A)  Circle 
B)  Ellipse 
C)  Parabola 
D)  Hyperbola 
E)  Line 
A)  Circle 
B)  Ellipse 
C)  Parabola 
D)  Hyperbola 
E)  Line

Question 14

Convert (2,   ,   ) from spherical to rectangular coordinates.

Accepted Answer

A)  (2, 2, 2) 
B)  (0, -2, 0) 
C)  (0, 0, 2) 
D)  (2, 0, 0) 
E)  (0, 0, 0) 
A)  (2, 2, 2) 
B)  (0, -2, 0) 
C)  (0, 0, 2) 
D)  (2, 0, 0) 
E)  (0, 0, 0)

Question 15

Lines   and   are

Accepted Answer

A)  intersecting at one point, but not perpendicular 
B)  skew 
C)  parallel 
D)  perpendicular 
E)  the same line 
A)  intersecting at one point, but not perpendicular 
B)  skew 
C)  parallel 
D)  perpendicular 
E)  the same line

Question 16

A particle is said to be in static equilibrium if the resultant of all forces applied to it is zero. Find the force F that must be applied to a particle to produce static equilibrium if there are two forces, each of 10 N, applied so that one acts   above the positive x-axis and the other acts   below the positive x-axis. Give the magnitude of the resultant, in newtons, acting in the negative x direction.

Accepted Answer

A)  10 
B)  20 
C)    
D)    
E)  40 
A)  10 
B)  20 
C)    
D)    
E)  40

Question 17

Identify the trace of the surface defined by   when   .

Accepted Answer

A)  Circle 
B)  Ellipse 
C)  Parabola 
D)  Hyperbola 
E)  Line 
A)  Circle 
B)  Ellipse 
C)  Parabola 
D)  Hyperbola 
E)  Line

Question 18

A parallelogram has   and   as adjacent sides. Find the area, in square units, of the parallelogram to 3 decimal place accuracy.

Accepted Answer

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

Question 19

Identify the quadratic surface defined by   .

Accepted Answer

A)  Ellipsoid 
B)  Hyperboloid of two sheets 
C)  Hyperboloid of one sheet 
D)  Hyperbolic paraboloid 
E)  Sphere 
A)  Ellipsoid 
B)  Hyperboloid of two sheets 
C)  Hyperboloid of one sheet 
D)  Hyperbolic paraboloid 
E)  Sphere

Question 20

Identify the quadratic surface defined by   .

Accepted Answer

A)  Ellipsoid 
B)  Elliptic cone 
C)  Elliptic paraboloid 
D)  Hyperbolic paraboloid 
E)  Sphere 
A)  Ellipsoid 
B)  Elliptic cone 
C)  Elliptic paraboloid 
D)  Hyperbolic paraboloid 
E)  Sphere

The equation for the cylinder with radius 4 oriented symmetric about the z-axis is

Identify the trace of the surface defined by when .

Find

If , , and , find and .

Identify the trace of the surface defined by when .

Convert from cylindrical to spherical coordinates.

What are the components of v. ?

Let . Find the vector in the same direction as u with twice the length of u.

At what point does the line intersect the plane containing the point (0, -1, 0) which is parallel to the xz- plane?

If , find

Let . Find the vector x that satisfies .

Find the angle between and .

Identify the trace of the surface defined by when .

Convert (2, , ) from spherical to rectangular coordinates.

Lines and are

Identify the trace of the surface defined by when .

A parallelogram has and as adjacent sides. Find the area, in square units, of the parallelogram to 3 decimal place accuracy.

Identify the quadratic surface defined by .

Identify the quadratic surface defined by .

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Exam 11: Three-Dimensional Space; Vectors

The equation for the cylinder with radius 4 oriented symmetric about the z-axis is

Identify the trace of the surface defined by when .

Find

If , , and , find and .

Identify the trace of the surface defined by when .

Convert from cylindrical to spherical coordinates.

What are the components of v. ?

Let . Find the vector in the same direction as u with twice the length of u.

At what point does the line intersect the plane containing the point (0, -1, 0) which is parallel to the xz- plane?

If , find

Let . Find the vector x that satisfies .

Find the angle between and .

Identify the trace of the surface defined by when .

Convert (2, , ) from spherical to rectangular coordinates.

Lines and are

Identify the trace of the surface defined by when .

A parallelogram has and as adjacent sides. Find the area, in square units, of the parallelogram to 3 decimal place accuracy.

Identify the quadratic surface defined by .

Identify the quadratic surface defined by .

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters