Question 1

Determine whether the following planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle of intersection.

Accepted Answer

A)  The planes are neither parallel nor orthogonal, the angle of intersection is   . 
B)  The planes are neither parallel nor orthogonal, the angle of intersection is   . 
C)  The planes are orthogonal. 
D)  The planes are parallel. 
A)  The planes are neither parallel nor orthogonal, the angle of intersection is   . 
B)  The planes are neither parallel nor orthogonal, the angle of intersection is   . 
C)  The planes are orthogonal. 
D)  The planes are parallel. A

Question 2

Find an equation of a plane passing through the following three points.

Accepted Answer

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

Question 3

Find an equation of a plane passing through the given point and perpendicular to the given vector. Point:   Vector:

Accepted Answer

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

Question 4

Find the area of the triangle with the vertices   and   . Round your answer to two decimal places.

Accepted Answer

A)  8.00 
B)  14.00 
C)  6.00 
D)  1.41 
E)  2.83 
A)  8.00 
B)  14.00 
C)  6.00 
D)  1.41 
E)  2.83

Question 5

Three forces with magnitudes   pounds,   pounds and   pounds act on an object at angles   ,   , and   respectively, with the positive x-axis. Find the direction and magnitude of the resultant force. (The choices below are given to two decimal places.)

Accepted Answer

A)    pounds at an angle of   with the positive x-axis 
B)    pounds at an angle of   with the positive x-axis 
C)    pounds at an angle of   with the positive x-axis 
D)    pounds at an angle of   with the positive x-axis 
E)    pounds at an angle of   with the positive x-axis 
A)    pounds at an angle of   with the positive x-axis 
B)    pounds at an angle of   with the positive x-axis 
C)    pounds at an angle of   with the positive x-axis 
D)    pounds at an angle of   with the positive x-axis 
E)    pounds at an angle of   with the positive x-axis

Question 6

Find an equation in rectangular coordinates for the equation given in cylindrical coordinates.

Accepted Answer

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

Question 7

Some planet is an oblate ellipsoid rather than a sphere because of the forces caused by its rotation. The equatorial radius of this planet is 4851 miles and the polar radius is 4660 miles. Find the equation of the ellipsoid. (Assume that the center of a planet is at the origin and that the trace formed by the plane   corresponds to the equator.)

Accepted Answer

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

Question 8

Convert the point   from rectangular coordinates to spherical coordinates.

Accepted Answer

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

Question 9

Given   , find   .

Accepted Answer

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

Question 10

Suppose a plane flies at a constant groundspeed of 300 miles per hour due east and encounters a 50 mile-per-hour wind from the northwest. Both the airspeed and the compass direction must change to for the plane to maintain its groundspeed and eastward direction. Find the airspeed to maintain its groundspeed and eastward direction. Round your answer to two decimal places. ​

Accepted Answer

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

Question 11

Find the coordinates of the point that is located 6 units behind the yz-plane, 5 units to the left of xz-plane, and 5 units below the xy-plane.

Accepted Answer

A)  (-6,-5,5) 
B)  (-6,5,-5) 
C)  (6,-5,-5) 
D)  (-6,5,5) 
E)  (-6,-5,-5) 
A)  (-6,-5,5) 
B)  (-6,5,-5) 
C)  (6,-5,-5) 
D)  (-6,5,5) 
E)  (-6,-5,-5)

Question 12

Find the vector v with the magnitude   and direction of   . ​
​

Accepted Answer

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

Question 13

Find a set of parametric equations of the line through the points   and   .

Accepted Answer

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

Question 14

Given the vector v lies in the yz-plane, has magnitude 2, and makes an angle of   with the positive y-axis. Find the component form of v.

Accepted Answer

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

Question 15

Find a set of parametric equations of the line that passes through the point   and is parallel to the xy-plane and yz-plane.

Accepted Answer

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

Question 16

Find vectors u and v whose initial and terminal points are given. Determine whether u and v are equivalent. ​
U: (4,2), (7,6) v: (-2,3), (1,7)
​

Accepted Answer

A)    , which are equivalent 
B)    , which are not equivalent 
C)    , which are equivalent 
D)    , which are equivalent 
E)    , which are equivalent 
A)    , which are equivalent 
B)    , which are not equivalent 
C)    , which are equivalent 
D)    , which are equivalent 
E)    , which are equivalent

Question 17

Find a set of parametric equations of the line through the point   parallel to the vector   .

Accepted Answer

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

Question 18

Find an equation in rectangular coordinates for the equation given in cylindrical coordinates.

Accepted Answer

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

Question 19

Suppose the guy wire to a 100-foot tower has a tension of 550 pounds. Using the distances shown in the figure, write the component form of the vector F representing the tension in the wire. Round numerical values in your answer to the nearest integer. ​   ​

Accepted Answer

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

Question 20

Determine whether the following planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle of intersection.

Accepted Answer

A)  The planes are neither parallel nor orthogonal, the angle of intersection is   . 
B)  The planes are parallel. 
C)  The planes are neither parallel nor orthogonal, the angle of intersection is   . 
D)  The planes are orthogonal. 
A)  The planes are neither parallel nor orthogonal, the angle of intersection is   . 
B)  The planes are parallel. 
C)  The planes are neither parallel nor orthogonal, the angle of intersection is   . 
D)  The planes are orthogonal.

Determine whether the following planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle of intersection.

Find an equation of a plane passing through the following three points.

Find an equation of a plane passing through the given point and perpendicular to the given vector. Point: Vector:

Find the area of the triangle with the vertices and . Round your answer to two decimal places.

Three forces with magnitudes pounds, pounds and pounds act on an object at angles , , and respectively, with the positive x-axis. Find the direction and magnitude of the resultant force. (The choices below are given to two decimal places.)

Find an equation in rectangular coordinates for the equation given in cylindrical coordinates.

Convert the point from rectangular coordinates to spherical coordinates.

Given , find .

Find the coordinates of the point that is located 6 units behind the yz-plane, 5 units to the left of xz-plane, and 5 units below the xy-plane.

Find the vector v with the magnitude and direction of .

Find a set of parametric equations of the line through the points and .

Given the vector v lies in the yz-plane, has magnitude 2, and makes an angle of with the positive y-axis. Find the component form of v.

Find a set of parametric equations of the line that passes through the point and is parallel to the xy-plane and yz-plane.

Find vectors u and v whose initial and terminal points are given. Determine whether u and v are equivalent. U: (4,2), (7,6) v: (-2,3), (1,7)

Find a set of parametric equations of the line through the point parallel to the vector .

Find an equation in rectangular coordinates for the equation given in cylindrical coordinates.

Suppose the guy wire to a 100-foot tower has a tension of 550 pounds. Using the distances shown in the figure, write the component form of the vector F representing the tension in the wire. Round numerical values in your answer to the nearest integer.

Determine whether the following planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle of intersection.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 11: Vectors and the Geometry of Space

Determine whether the following planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle of intersection.

Find an equation of a plane passing through the following three points.

Find an equation of a plane passing through the given point and perpendicular to the given vector. Point: Vector:

Find the area of the triangle with the vertices and . Round your answer to two decimal places.

Three forces with magnitudes pounds, pounds and pounds act on an object at angles , , and respectively, with the positive x-axis. Find the direction and magnitude of the resultant force. (The choices below are given to two decimal places.)

Find an equation in rectangular coordinates for the equation given in cylindrical coordinates.

Convert the point from rectangular coordinates to spherical coordinates.

Given , find .

Find the coordinates of the point that is located 6 units behind the yz-plane, 5 units to the left of xz-plane, and 5 units below the xy-plane.

Find the vector v with the magnitude and direction of . ​ ​

Find a set of parametric equations of the line through the points and .

Given the vector v lies in the yz-plane, has magnitude 2, and makes an angle of with the positive y-axis. Find the component form of v.

Find a set of parametric equations of the line that passes through the point and is parallel to the xy-plane and yz-plane.

Find vectors u and v whose initial and terminal points are given. Determine whether u and v are equivalent. ​ U: (4,2), (7,6) v: (-2,3), (1,7) ​

Find a set of parametric equations of the line through the point parallel to the vector .

Find an equation in rectangular coordinates for the equation given in cylindrical coordinates.

Suppose the guy wire to a 100-foot tower has a tension of 550 pounds. Using the distances shown in the figure, write the component form of the vector F representing the tension in the wire. Round numerical values in your answer to the nearest integer. ​ ​

Determine whether the following planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle of intersection.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Find the vector v with the magnitude and direction of .

Find vectors u and v whose initial and terminal points are given. Determine whether u and v are equivalent. U: (4,2), (7,6) v: (-2,3), (1,7)

Suppose the guy wire to a 100-foot tower has a tension of 550 pounds. Using the distances shown in the figure, write the component form of the vector F representing the tension in the wire. Round numerical values in your answer to the nearest integer.