Question 1

Find an equation for the surface consisting of all points that are equidistant from the point   and the plane   Select the correct Answer

Accepted Answer

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

Question 2

Find the distance from   to the xy-planes.Select the correct Answer

Accepted Answer

A) 8 
B) 16 
C) 10 
D) 2 
E) 4 
A) 8 
B) 16 
C) 10 
D) 2 
E) 4

Question 3

Find the center and the radius of the sphere that has the given equation.

Accepted Answer

The answer of Find the center and the radius of...

Question 4

Find the work done by a force   that moves an object from the point   to the point   along a straight line.The distance is measured in meters and the force in newtons.

Accepted Answer

The answer of Find the work done by a force...

Question 5

Find the point of intersection.

Accepted Answer

The answer of Find the point of intersection.  ...

Question 6

Classify the surface.   Select the correct Answer

Accepted Answer

A) A hyperboloid of one sheet with center   and axis parallel to the   
B) A circular paraboloid with vertex   and axis the   
C) A cone with axis parallel to the   -axis and vertex   
A) A hyperboloid of one sheet with center   and axis parallel to the   
B) A circular paraboloid with vertex   and axis the   
C) A cone with axis parallel to the   -axis and vertex

Question 7

Select the correct Answer for each question.
-Which of the given lines is parallel to the line

Accepted Answer

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

Question 8

Classify the surface.

Accepted Answer

A cone with axis par

Question 9

Calculate the angle between a and b (correct to the nearest degree).

Accepted Answer

The answer of Calculate the angle between a and b...

Question 10

Calculate the angle between a and b (correct to the nearest degree).

Accepted Answer

The answer of Calculate the angle between a and b...

Question 11

Find the point of intersection.

Accepted Answer

The answer of Find the point of intersection.  ...

Question 12

Select the correct Answer: for each question.
-Find the cross product

Accepted Answer

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

Question 13

Identify the planes that are perpendicular.Select the correct Answer

Accepted Answer

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

Question 14

Find the distance between the point   and the plane   Round yourAnswer to two decimal place.Select the correct Answer

Accepted Answer

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

Question 15

Select the correct Answer for each question.
-Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is   times the distance from P to the

Accepted Answer

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

Question 16

Select the correct Answer: for each question.
-Let   and let u be a vector with length   that starts at the origin and rotates in the xy - plane.Find the maximum value of the length of the vector

Accepted Answer

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

Question 17

Find the equation of the line through   and perpendicular to the plane

Accepted Answer

The answer of Find the equation of the line through...

Question 18

Find, correct to the nearest degree, the angle between the planes.

Accepted Answer

The answer of Find, correct to the nearest degree, the...

Question 19

Reduce the equation to one of the standard forms.

Accepted Answer

The answer of Reduce the equation to one of the...

Question 20

Find an equation of the plane that passes through the line of intersection of the planes   and   is perpendicular to the plane

Accepted Answer

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

Find an equation for the surface consisting of all points that are equidistant from the point and the plane Select the correct Answer

Find the distance from to the xy-planes.Select the correct Answer

Find the center and the radius of the sphere that has the given equation.

Find the work done by a force that moves an object from the point to the point along a straight line.The distance is measured in meters and the force in newtons.

Find the point of intersection.

Classify the surface. Select the correct Answer

Select the correct Answer for each question. -Which of the given lines is parallel to the line

Classify the surface.

Calculate the angle between a and b (correct to the nearest degree).

Calculate the angle between a and b (correct to the nearest degree).

Find the point of intersection.

Select the correct Answer: for each question. -Find the cross product

Identify the planes that are perpendicular.Select the correct Answer

Find the distance between the point and the plane Round yourAnswer to two decimal place.Select the correct Answer

Select the correct Answer for each question. -Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is times the distance from P to the

Select the correct Answer: for each question. -Let and let u be a vector with length that starts at the origin and rotates in the xy - plane.Find the maximum value of the length of the vector

Find the equation of the line through and perpendicular to the plane

Find, correct to the nearest degree, the angle between the planes.

Reduce the equation to one of the standard forms.

Find an equation of the plane that passes through the line of intersection of the planes and is perpendicular to the plane

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters

Exam 12: Vectors and the Geometry of Space

Find an equation for the surface consisting of all points that are equidistant from the point and the plane Select the correct Answer

Find the distance from to the xy-planes.Select the correct Answer

Find the center and the radius of the sphere that has the given equation.

Find the work done by a force that moves an object from the point to the point along a straight line.The distance is measured in meters and the force in newtons.

Find the point of intersection.

Classify the surface. Select the correct Answer

Select the correct Answer for each question. -Which of the given lines is parallel to the line

Classify the surface.

Calculate the angle between a and b (correct to the nearest degree).

Calculate the angle between a and b (correct to the nearest degree).

Find the point of intersection.

Select the correct Answer: for each question. -Find the cross product

Identify the planes that are perpendicular.Select the correct Answer

Find the distance between the point and the plane Round yourAnswer to two decimal place.Select the correct Answer

Select the correct Answer for each question. -Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is times the distance from P to the

Select the correct Answer: for each question. -Let and let u be a vector with length that starts at the origin and rotates in the xy - plane.Find the maximum value of the length of the vector

Find the equation of the line through and perpendicular to the plane

Find, correct to the nearest degree, the angle between the planes.

Reduce the equation to one of the standard forms.

Find an equation of the plane that passes through the line of intersection of the planes and is perpendicular to the plane

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters