Question 1

Determine whether the given points are collinear. A (-3, -2, -3), B (-9, -5, 0), and C (-1, -1, -4)

Accepted Answer

A) Collinear 
B) Not collinear 
A) Collinear 
B) Not collinear

Question 2

Calculate the given quantities if

Accepted Answer

The answer of Calculate the given quantities if  ...

Question 3

Write an inequality to describe the region consisting of all points between (but not on) the
spheres of radius   and   centered at the origin.

Accepted Answer

The answer of Write an inequality to describe the region...

Question 4

Find an equation of the sphere with center   that touches the xy-plane.

Accepted Answer

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

Question 5

a.Find an equation of the sphere that passes through the point   and has center   . 
b.Find the curve in which this sphere intersects the xy-plane.

Accepted Answer

The answer of a.Find an equation of the sphere that...

Question 6

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 7

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...

Question 8

Sketch the plane in a three-dimensional space represented by the equation. z = 2

Accepted Answer

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

Question 9

Two forces   with magnitudes 8 lb and 12 lb act on an object at a point P as shown in the figure. Find the magnitude of the resultant force F acting at P. Round the result to the nearest tenth.

Accepted Answer

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

Question 10

Find   correct to three decimal places where   ,   ,   .

Accepted Answer

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

Question 11

Reduce the equation to one of the standard forms.

Accepted Answer

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

Question 12

Find an equation of the sphere that passes through the point   and has center   .

Accepted Answer

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

Question 13

Find the standard equation of the sphere with center C and radius r. C (3, -5, 3); r = 7

Accepted Answer

A) (x - 3)2 + (y + 5)2 + (z - 3)2 = 7 
B) (x - 3)2 + (y + 5)2 + (z - 3)2 = 49 
C) (x + 3)2 + (y - 5)2 + (z + 3)2 = 7 
D) (x + 3)2 + (y - 5)2 + (z + 3)2 = 49 
A) (x - 3)2 + (y + 5)2 + (z - 3)2 = 7 
B) (x - 3)2 + (y + 5)2 + (z - 3)2 = 49 
C) (x + 3)2 + (y - 5)2 + (z + 3)2 = 7 
D) (x + 3)2 + (y - 5)2 + (z + 3)2 = 49

Question 14

Find the magnitude of the torque about P correct to two decimal places if a d-lb force is applied as shown. Let   ft,   ft,   ,   lb.

Accepted Answer

The answer of Find the magnitude of the torque about...

Question 15

Find an equation of the plane that passes through the point   and contains the line

Accepted Answer

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

Question 16

Find the center and the radius of the sphere that has the given equation.   +   +   - 6x + 4y = 0

Accepted Answer

A) ( -3, 2, 0),   
B) ( 3, -2, 0), 13 
C) ( -3, 2, 0), 13 
D) ( 3, -2, 0),   
A) ( -3, 2, 0),   
B) ( 3, -2, 0), 13 
C) ( -3, 2, 0), 13 
D) ( 3, -2, 0),

Question 17

Find the distance from   to the xy-planes.

Accepted Answer

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

Question 18

Plot the given points in a three-dimensional coordinate system. (1, 2, 3)

Accepted Answer

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

Question 19

Identify the planes that are perpendicular.

Accepted Answer

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

Question 20

Find that the midpoint of the line segment from   to   .

Accepted Answer

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

Determine whether the given points are collinear. A (-3, -2, -3), B (-9, -5, 0), and C (-1, -1, -4)

Calculate the given quantities if

Write an inequality to describe the region consisting of all points between (but not on) the spheres of radius and centered at the origin.

Find an equation of the sphere with center that touches the xy-plane.

a.Find an equation of the sphere that passes through the point and has center . b.Find the curve in which this sphere intersects the xy-plane.

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.

Sketch the plane in a three-dimensional space represented by the equation. z = 2

Two forces with magnitudes 8 lb and 12 lb act on an object at a point P as shown in the figure. Find the magnitude of the resultant force F acting at P. Round the result to the nearest tenth.

Find correct to three decimal places where , , .

Reduce the equation to one of the standard forms.

Find an equation of the sphere that passes through the point and has center .

Find the standard equation of the sphere with center C and radius r. C (3, -5, 3); r = 7

Find the magnitude of the torque about P correct to two decimal places if a d-lb force is applied as shown. Let ft, ft, , lb.

Find an equation of the plane that passes through the point and contains the line

Find the center and the radius of the sphere that has the given equation. + + - 6x + 4y = 0

Find the distance from to the xy-planes.

Plot the given points in a three-dimensional coordinate system. (1, 2, 3)

Identify the planes that are perpendicular.

Find that the midpoint of the line segment from to .

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

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

Final Exam

Filters

Exam 12: Vectors and the Geometry of Space

Determine whether the given points are collinear. A (-3, -2, -3), B (-9, -5, 0), and C (-1, -1, -4)

Calculate the given quantities if

Write an inequality to describe the region consisting of all points between (but not on) the spheres of radius and centered at the origin.

Find an equation of the sphere with center that touches the xy-plane.

a.Find an equation of the sphere that passes through the point and has center . b.Find the curve in which this sphere intersects the xy-plane.

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.

Sketch the plane in a three-dimensional space represented by the equation. z = 2

Two forces with magnitudes 8 lb and 12 lb act on an object at a point P as shown in the figure. Find the magnitude of the resultant force F acting at P. Round the result to the nearest tenth.

Find correct to three decimal places where , , .

Reduce the equation to one of the standard forms.

Find an equation of the sphere that passes through the point and has center .

Find the standard equation of the sphere with center C and radius r. C (3, -5, 3); r = 7

Find the magnitude of the torque about P correct to two decimal places if a d-lb force is applied as shown. Let ft, ft, , lb.

Find an equation of the plane that passes through the point and contains the line

Find the center and the radius of the sphere that has the given equation. + + - 6x + 4y = 0

Find the distance from to the xy-planes.

Plot the given points in a three-dimensional coordinate system. (1, 2, 3)

Identify the planes that are perpendicular.

Find that the midpoint of the line segment from to .

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

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

Final Exam

Filters