Question 1

Select the correct Answer for each question.
-Sketch the plane in a three-dimensional space represented by the equation.

Accepted Answer

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

Question 2

Find the length of the median of side AB of the triangle with vertices

Accepted Answer

The answer of Find the length of the median of...

Question 3

Select the correct Answer for each question.
-Find the midpoint of the line segment joining the given points.

Accepted Answer

A)    
B) (-1, 1, -1) 
C)    
D) (-1, 1, -2) 
A)    
B) (-1, 1, -1) 
C)    
D) (-1, 1, -2)

Question 4

Calculate the given quantities if

Accepted Answer

The answer of Calculate the given quantities if  ...

Question 5

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

The answer of Find an equation for the surface consisting...

Question 6

Find parametric equations for the line through the point   that is parallel to the plane   and perpendicular to the line   Select the correct Answer

Accepted Answer

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

Question 7

Select the correct Answer: for each question.
-Find the distance from   to the xy-planes.

Accepted Answer

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

Question 8

Find the cross product

Accepted Answer

The answer of Find the cross product   ...

Question 9

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.Select the correct Answer

Accepted Answer

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

Question 10

Find the standard equation of the sphere with center C and radius r.C (4, -1, 1); r = 6

Accepted Answer

The answer of Find the standard equation of the sphere...

Question 11

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

Accepted Answer

The answer of Find an equation for the surface consisting...

Question 12

Select the correct Answer: for each question.
-Find the unit vectors that are parallel to the tangent line to the curve   at the point

Accepted Answer

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

Question 13

Select the correct Answer for each question.
-Find the center and the radius of the sphere that has the given equation.

Accepted Answer

A)    
B) ( -2, 4, 0), 20 
C)    
D) ( 2, -4, 0), 20 
A)    
B) ( -2, 4, 0), 20 
C)    
D) ( 2, -4, 0), 20

Question 14

Find the point at which the line given by the parametric equations below intersects the plane.   Select the correct Answer

Accepted Answer

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

Question 15

Find parametric equations for the line through the point   that is parallel to the plane and perpendicular to the line

Accepted Answer

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

Question 16

A bicycle pedal is pushed by a foot with a force of   as shown.The shaft of the pedal is   long.Find the magnitude of the torque about P correct to two decimal places.

Accepted Answer

The answer of A bicycle pedal is pushed by a...

Question 17

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

Accepted Answer

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

Question 18

Find the point at which the line given by the parametric equations below intersects the plane.

Accepted Answer

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

Question 19

Select the correct Answer: for each question.
-Find parametric equations for the line through the point   that is parallel to the plane   and perpendicular to the line

Accepted Answer

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

Question 20

Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS.

Accepted Answer

The answer of Find the volume of the parallelepiped with...

Select the correct Answer for each question. -Sketch the plane in a three-dimensional space represented by the equation.

Find the length of the median of side AB of the triangle with vertices

Select the correct Answer for each question. -Find the midpoint of the line segment joining the given points.

Calculate the given quantities if

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

Find parametric equations for the line through the point that is parallel to the plane and perpendicular to the line Select the correct Answer

Select the correct Answer: for each question. -Find the distance from to the xy-planes.

Find the cross product

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.Select the correct Answer

Find the standard equation of the sphere with center C and radius r.C (4, -1, 1); r = 6

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

Select the correct Answer: for each question. -Find the unit vectors that are parallel to the tangent line to the curve at the point

Select the correct Answer for each question. -Find the center and the radius of the sphere that has the given equation.

Find the point at which the line given by the parametric equations below intersects the plane. Select the correct Answer

Find parametric equations for the line through the point that is parallel to the plane and perpendicular to the line

A bicycle pedal is pushed by a foot with a force of as shown.The shaft of the pedal is long.Find the magnitude of the torque about P correct to two decimal places.

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

Find the point at which the line given by the parametric equations below intersects the plane.

Select the correct Answer: for each question. -Find parametric equations for the line through the point that is parallel to the plane and perpendicular to the line

Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS.

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

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Exam 12: Vectors and the Geometry of Space

Select the correct Answer for each question. -Sketch the plane in a three-dimensional space represented by the equation.

Find the length of the median of side AB of the triangle with vertices

Select the correct Answer for each question. -Find the midpoint of the line segment joining the given points.

Calculate the given quantities if

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

Find parametric equations for the line through the point that is parallel to the plane and perpendicular to the line Select the correct Answer

Select the correct Answer: for each question. -Find the distance from to the xy-planes.

Find the cross product

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.Select the correct Answer

Find the standard equation of the sphere with center C and radius r.C (4, -1, 1); r = 6

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

Select the correct Answer: for each question. -Find the unit vectors that are parallel to the tangent line to the curve at the point

Select the correct Answer for each question. -Find the center and the radius of the sphere that has the given equation.

Find the point at which the line given by the parametric equations below intersects the plane. Select the correct Answer

Find parametric equations for the line through the point that is parallel to the plane and perpendicular to the line

A bicycle pedal is pushed by a foot with a force of as shown.The shaft of the pedal is long.Find the magnitude of the torque about P correct to two decimal places.

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

Find the point at which the line given by the parametric equations below intersects the plane.

Select the correct Answer: for each question. -Find parametric equations for the line through the point that is parallel to the plane and perpendicular to the line

Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS.

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