Question 1

Find the scalar triple product for the vectors

Accepted Answer

A)  -304 
B)  -392 
C)  -44 
D)  304 
E)  0 
A)  -304 
B)  -392 
C)  -44 
D)  304 
E)  0

Question 2

Find the acute angle of intersection of   and   (Round answer to the nearest degree.)

Accepted Answer

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

Question 3

Find the dot product   .

Accepted Answer

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

Question 4

Find the distance from the surface   to (9, 0, 0).

Accepted Answer

The answer of Find the distance from the surface ...

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

Find the parametric equations for the line through the point   parallel to the vector

Accepted Answer

A)    
B)    
C)    
D)    , z = 1 
E)    
A)    
B)    
C)    
D)    , z = 1 
E)

Question 7

If

Accepted Answer

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

Question 8

Find the parametric equations for the line passing through   and   .

Accepted Answer

The answer of Find the parametric equations for the line...

Question 9

Find the direction vector for the line joining the points   and   .

Accepted Answer

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

Question 10

The distance from (5, 7, 10) to the xz-plane is

Accepted Answer

A)  5 
B)  7 
C)  10 
D)  13.190906 
E)  8.602325 
A)  5 
B)  7 
C)  10 
D)  13.190906 
E)  8.602325

Question 11

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

Question 12

If

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)  There is no trace. 
A)  Circle 
B)  Ellipse 
C)  Parabola 
D)  Hyperbola 
E)  There is no trace.

Question 14

A plane is perpendicular to the line given by   ,   , and   . What are the components of the normal to the plane?

Accepted Answer

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

Question 15

The distance from (2, 4, 7) to the xy-plane is

Accepted Answer

A)  2 
B)  4 
C)  7 
D)  8.306624 
E)  4.472136 
A)  2 
B)  4 
C)  7 
D)  8.306624 
E)  4.472136

Question 16

Find the point of intersection of the lines

Accepted Answer

A)  (9, 0, 63) 
B)    
C)  (2, -8, 7) 
D)  (0, 0,0) 
E)  (1, 1, 1) 
A)  (9, 0, 63) 
B)    
C)  (2, -8, 7) 
D)  (0, 0,0) 
E)  (1, 1, 1)

Question 17

Find the parametric equations for the line passing through   and   .

Accepted Answer

The answer of Find the parametric equations for the line...

Question 18

Let   . Find the length of u.

Accepted Answer

The answer of Let   . Find the length...

Question 19

Find the direction cosines of the vector   .

Accepted Answer

The answer of Find the direction cosines of the vector...

Question 20

Find the distance between the point   and   . Approximate your answer to 4 decimal places.

Accepted Answer

The answer of Find the distance between the point ...

Find the scalar triple product for the vectors

Find the acute angle of intersection of and (Round answer to the nearest degree.)

Find the dot product .

Find the distance from the surface to (9, 0, 0).

Identify the trace of the surface defined by when .

Find the parametric equations for the line through the point parallel to the vector

If

Find the parametric equations for the line passing through and .

Find the direction vector for the line joining the points and .

The distance from (5, 7, 10) to the xz-plane is

Identify the quadratic surface defined by .

If

Identify the trace of the surface defined by when .

A plane is perpendicular to the line given by , , and . What are the components of the normal to the plane?

The distance from (2, 4, 7) to the xy-plane is

Find the point of intersection of the lines

Find the parametric equations for the line passing through and .

Let . Find the length of u.

Find the direction cosines of the vector .

Find the distance between the point and . Approximate your answer to 4 decimal places.

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

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Exam 11: Three-Dimensional Space; Vectors

Find the scalar triple product for the vectors

Find the acute angle of intersection of and (Round answer to the nearest degree.)

Find the dot product .

Find the distance from the surface to (9, 0, 0).

Identify the trace of the surface defined by when .

Find the parametric equations for the line through the point parallel to the vector

If

Find the parametric equations for the line passing through and .

Find the direction vector for the line joining the points and .

The distance from (5, 7, 10) to the xz-plane is

Identify the quadratic surface defined by .

If

Identify the trace of the surface defined by when .

A plane is perpendicular to the line given by , , and . What are the components of the normal to the plane?

The distance from (2, 4, 7) to the xy-plane is

Find the point of intersection of the lines

Find the parametric equations for the line passing through and .

Let . Find the length of u.

Find the direction cosines of the vector .

Find the distance between the point and . Approximate your answer to 4 decimal places.

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