Question 1

Determine whether the lines given below intersect, and, if so, find the point of intersection.

Accepted Answer

A)  The lines are parallel. 
B)  The lines intersect at   . 
C)  The lines intersect at   . 
D)  The lines intersect at   . 
E)  The lines are not parallel but do not intersect. 
A)  The lines are parallel. 
B)  The lines intersect at   . 
C)  The lines intersect at   . 
D)  The lines intersect at   . 
E)  The lines are not parallel but do not intersect. D

Question 2

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)    A

Question 3

Find an equation of a plane passing through the points   and perpendicular to the plane   .

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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)

Question 6

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.

Question 7

Determine whether any of the lines given below are parallel or identical.

Accepted Answer

A)    are parallel 
B)    are identical 
C)    are parallel 
D)    are identical 
E)    are parallel 
A)    are parallel 
B)    are identical 
C)    are parallel 
D)    are identical 
E)    are parallel

Question 8

Find the distance between the point   and the line given by the set of parametric equations   .

Accepted Answer

A)    /11 
B)  2 
C)    /11 
D)  4 
E)  1 
A)    /11 
B)  2 
C)    /11 
D)  4 
E)  1

Question 9

Determine whether any of the lines given below are parallel or identical.

Accepted Answer

A)    are identical 
B)    are identical 
C)    are identical 
D)    are parallel 
E)    are parallel 
A)    are identical 
B)    are identical 
C)    are identical 
D)    are parallel 
E)    are parallel

Question 10

A chute at the top of a grain elevator of a combine funnels the grain into a bin (see figure). Find the angle between two adjacent sides. Round your answer to one decimal place.

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

Find the distance between the planes given below.

Accepted Answer

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

Question 13

Determine whether the lines given below intersect, and, if so, find the point of intersection.

Accepted Answer

A)  The lines intersect at   . 
B)  The lines are parallel. 
C)  The lines intersect at   . 
D)  The lines intersect at   . 
E)  The lines are not parallel but do not intersect. 
A)  The lines intersect at   . 
B)  The lines are parallel. 
C)  The lines intersect at   . 
D)  The lines intersect at   . 
E)  The lines are not parallel but do not intersect.

Question 14

Two insects are crawling along different lines in three-space. At time t (in minutes), the first insect is at the point   where   . Also, at time t, the second insect is at the point   where   . Assume distances are given in inches. How close do the insects get? Round your answer to two decimal places.

Accepted Answer

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

Question 15

Find the set of parametric equations of the line through the point   that is parallel to the line   ,   ,and   .

Accepted Answer

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

Question 16

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 17

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

Accepted Answer

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

Question 18

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.

Question 19

Find the distance between the point   and the plane   .

Accepted Answer

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

Question 20

Two insects are crawling along different lines in three-space. At time t (in minutes), the first insect is at the point   where   . Also, at time t, the second insect is at the point   where   . Assume distances are given in inches. Find the distance between the two insects at time   . Round your answer to two decimal places.

Accepted Answer

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

Exam 11: Section 5: Vectors and the Geometry of Space

Determine whether the lines given below intersect, and, if so, find the point of intersection.

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 an equation of a plane passing through the points and perpendicular to the plane .

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

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

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

Determine whether any of the lines given below are parallel or identical.

Find the distance between the point and the line given by the set of parametric equations .

Determine whether any of the lines given below are parallel or identical.

A chute at the top of a grain elevator of a combine funnels the grain into a bin (see figure). Find the angle between two adjacent sides. Round your answer to one decimal place.

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

Find the distance between the planes given below.

Determine whether the lines given below intersect, and, if so, find the point of intersection.

Two insects are crawling along different lines in three-space. At time t (in minutes), the first insect is at the point where . Also, at time t, the second insect is at the point where . Assume distances are given in inches. How close do the insects get? Round your answer to two decimal places.

Find the set of parametric equations of the line through the point that is parallel to the line , ,and .

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

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

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

Find the distance between the point and the plane .

Section 1: Preparation for Calculus

Section 2: Preparation for Calculus

Section 3: Preparation for Calculus

Section 4: Preparation for Calculus

Section 5: Preparation for Calculus

Section 6: Preparation for Calculus

Section 1: Limits and Their Properties

Section 2: Limits and Their Properties

Section 3: Limits and Their Properties

Section 4: Limits and Their Properties

Section 5 : Limits and Their Properties

Section 1 : Differentiation

Section 2: Differentiation

Section 3: Differentiation

Section 4 : Differentiation

Section 5: Differentiation

Section 6: Differentiation

Section 7: Differentiation

Section 8: Differentiation

Section 1 : Applications of Differentiation

Section 2: Applications of Differentiation

Section 3: Applications of Differentiation

Section 4: Applications of Differentiation

Section 5: Applications of Differentiation

Section 6: Applications of Differentiation

Section 7: Applications of Differentiation

Section 8: Applications of Differentiation

Section 1: Integration

Section 2: Integration

Section 3: Integration

Section 4: Integration

Section 5: Integration

Section 6: Integration

Section 7: Integration

Section 8: Integration

Section 9: Integration

Section 1: Differential Equations

Section 2: Differential Equations

Section 3: Differential Equations

Section 4: Differential Equations

Section 5: Differential Equations

Section 1: Applications of Integration

Section 2: Applications of Integration

Section 3: Applications of Integration

Section 4: Applications of Integration

Section 5: Applications of Integration

Section 6: Applications of Integration

Section 7: Applications of Integration

Section 1: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 2: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 3: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 4: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 5: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 6: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 7: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 8: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 1: Infinite Series

Section 2: Infinite Series

Section 3: Infinite Series

Section 4: Infinite Series