Question 1

Find an equation of the plane that passes through  and has the vector   as a normal vector.

Accepted Answer

The answer of Find an equation of the plane that...

Question 2

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

Accepted Answer

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

Question 3

Find the dot product   .

Accepted Answer

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

Question 4

Find the parametric equations for the line tangent to the circle   at the point   .

Accepted Answer

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

Question 5

The distance between the point (5, 6, 4) and   is

Accepted Answer

A)  4 
B)  3 
C)  -4 
D)  -3 
E)    
A)  4 
B)  3 
C)  -4 
D)  -3 
E)

Question 6

Find the angle between   and   . Approximate your answer to 1 decimal place.

Accepted Answer

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

Question 7

The equation of a surface is given in rectangular coordinates. Give the equation of the surface in cylindrical coordinates.

Accepted Answer

The answer of The equation of a surface is given...

Question 8

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

Accepted Answer

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

Question 9

The sphere represented by   has center

Accepted Answer

A)    
B)  (0, 0, 0) 
C)    
D)  (4, 6, 0) 
E)    
A)    
B)  (0, 0, 0) 
C)    
D)  (4, 6, 0) 
E)

Question 10

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

Accepted Answer

A)  (-1, 8, 17) 
B)  (-1, 0,1) 
C)  (0, -6, 17) 
D)  (-1, -6, 17) 
E)  (2, 8, 1) 
A)  (-1, 8, 17) 
B)  (-1, 0,1) 
C)  (0, -6, 17) 
D)  (-1, -6, 17) 
E)  (2, 8, 1)

Question 11

Determine if the three vectors , , and  are coplanar.

Accepted Answer

The answer of Determine if the three vectors , ,...

Question 12

Find a unit vector in the direction of   .

Accepted Answer

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

Question 13

The distance from (4, 0, 3) to the origin is

Accepted Answer

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

Question 14

The equation of a surface is given in rectangular coordinates. Give the equation of the surface in cylindrical coordinates.

Accepted Answer

The answer of The equation of a surface is given...

Question 15

Find the point of intersection of the two lines L1:  
  and L2:

Accepted Answer

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

Question 16

What are the components of v.   ?

Accepted Answer

A)  9 and -7 
B)  -7 and 2 
C)  2 and 16 
D)  0 and 0 
E)    and 0 
A)  9 and -7 
B)  -7 and 2 
C)  2 and 16 
D)  0 and 0 
E)    and 0

Question 17

Find the point where the line which passes through (3, 6, 8) and is parallel to   intersects the xz-plane.

Accepted Answer

The answer of Find the point where the line which...

Question 18

Identify the quadratic surface defined by   .

Accepted Answer

Hyperboloi

Question 19

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

Accepted Answer

A)  (4, -6, 1) 
B)  (5, 0,1) 
C)  (-13, 6, 1) 
D)  (-14, -5, 1) 
E)  (2, -6, 1) 
A)  (4, -6, 1) 
B)  (5, 0,1) 
C)  (-13, 6, 1) 
D)  (-14, -5, 1) 
E)  (2, -6, 1)

Question 20

Convert   from spherical to rectangular coordinates.

Accepted Answer

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

Find an equation of the plane that passes through <4, 5, 3> and has the vector as a normal vector.

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

Find the dot product .

Find the parametric equations for the line tangent to the circle at the point .

The distance between the point (5, 6, 4) and is

Find the angle between and . Approximate your answer to 1 decimal place.

The equation of a surface is given in rectangular coordinates. Give the equation of the surface in cylindrical coordinates.

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

The sphere represented by has center

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

Determine if the three vectors <4, 0, 0>, <0, 6, 8>, and <4, 6, 8> are coplanar.

Find a unit vector in the direction of .

The distance from (4, 0, 3) to the origin is

The equation of a surface is given in rectangular coordinates. Give the equation of the surface in cylindrical coordinates.

Find the point of intersection of the two lines L_1: and L₂:

What are the components of v. ?

Find the point where the line which passes through (3, 6, 8) and is parallel to intersects the xz-plane.

Identify the quadratic surface defined by .

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

Convert from spherical to rectangular coordinates.

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

Find an equation of the plane that passes through <4, 5, 3> and has the vector as a normal vector.

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

Find the dot product .

Find the parametric equations for the line tangent to the circle at the point .

The distance between the point (5, 6, 4) and is

Find the angle between and . Approximate your answer to 1 decimal place.

The equation of a surface is given in rectangular coordinates. Give the equation of the surface in cylindrical coordinates.

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

The sphere represented by has center

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

Determine if the three vectors <4, 0, 0>, <0, 6, 8>, and <4, 6, 8> are coplanar.

Find a unit vector in the direction of .

The distance from (4, 0, 3) to the origin is

The equation of a surface is given in rectangular coordinates. Give the equation of the surface in cylindrical coordinates.

Find the point of intersection of the two lines L1: and L2:

What are the components of v. ?

Find the point where the line which passes through (3, 6, 8) and is parallel to intersects the xz-plane.

Identify the quadratic surface defined by .

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

Convert from spherical to rectangular coordinates.

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

Find the point of intersection of the two lines L_1: and L₂: