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Damiano and Freije - Multivariable Calculus (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 3 / 36

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5 6 7
3/3 –/8 –/3 –/9 –/3 –/4 –/6
Total
3/36 (8.3%)

  • Instructions

    Here are some textbook questions from Multivariable Calculus 1/e by David B. Damiano and Margaret N. Freije published by Jones & Bartlett Learning. Click here for a list of all of the questions coded in WebAssign. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

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1. 3/3 points  |  Previous Answers DamianoMVCalc1 1.4.001. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 1/1 1/1
4/50 1/50 1/50
Total
3/3
 
Give the vector description of each of the following lines and the coordinate form for a point on the line. (Enter your answer as a single vector.)
(a) The line through P = (1, 2) with direction vector (−1, 1).
x
=
(1−t,2+t)
Correct: Your answer is correct. , t is in the set of real numbers

(b) The line through P = (−1, 2, 3) with direction vector (0, −1, 1).
x
=
(−1,2−t,3+t)
Correct: Your answer is correct. , t is in the set of real numbers

(c) The line through P = (4, 2, 0) and parallel to the line {x : x = (−1, 4, 2) + t(3, 1, 4), t is in the set of real numbers}.
x
=
(4+3t,2+t,4t)
Correct: Your answer is correct. , t is in the set of real numbers
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2. –/8 points DamianoMVCalc1 1.4.002. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8
–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
Total
–/8
 
Determine if each of the given points Q lies on the given line. If not, find a line through Q parallel to the given line. (Enter your answer as a single vector. If Q lies on the given line, enter that line.)
(a)    Q = (1, −2) and L is the line {x : x = (0, −3) + t(3, 2), t is in the set of real numbers}.
    

x =
, t is in the set of real numbers

(b)    Q = (−2, 4) and L is the line {(x, y) : x = 1 + 3t, y = 3 − t, t is in the set of real numbers}.
    

x =
, t is in the set of real numbers

(c)    Q = (−1, −3, 4) and L is the line {x : x = (0, −1, 3) + t(2, 4, −2), t is in the set of real numbers}.
    

x =
, t is in the set of real numbers

(d)    Q = (1, 2, 1) and L is the line {(x, y, z) : x = 1 + t, y = 3 − 2t, z = −1 − t, t is in the set of real numbers}.
    

x =
, t is in the set of real numbers
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3. –/3 points DamianoMVCalc1 1.4.007. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
(a) Given two lines L1 and L2 in the set of real numbers3, carefully describe how you would determine if the two lines intersect.

This answer has not been graded yet.



(b) Do the following pairs of lines intersect?
(i) The line through P = (−1, 3, 2) with direction vector (0, −1, 1) and the line through Q = (3, 4, −1) with direction vector (2, 1, −2).
    

(ii) The line through P = (1, 0, −1) with direction vector (−1, 2, 1) and the line through Q = (0, 2, 2) with direction vector (2, 1, −1).
    
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4. –/9 points DamianoMVCalc1 1.4.008. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9
–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
Total
–/9
 
Two distinct lines in the set of real numbers3 are parallel, skew, or intersect in a single point. If they intersect, the angle between the lines is defined to be the angle θ, 0 ≤ θ ≤ π/2, made by the lines at the point of intersection.
(a) If L1 and L2 intersect, how would you determine the angle between the two lines?

This answer has not been graded yet.



(b) Determine if the following pairs of lines in the set of real numbers3 are parallel, skew, or intersecting. If the lines intersect, find the angle between them. (Round your answers to two decimal places. If an answer does not exist, enter DNE.)
(i) The line through (−1, 2, 2) with direction vector (3, −1, 2) and the line through (2, 1, 4) with direction vector (0, 4, 2).
    

θ =


(ii)    
{(x, y, z) : x = 1 + s, y = 2 − s, z = 5 + 2s, s is in the set of real numbers}
 and
{(x, y, z) : x = 2t, y = 1 − 2t, z = 5 + 4t, t is in the set of real numbers}.

    

θ =


(iii)    
{x : x = (1, 1, 3) + s(1, −1, 2), s is in the set of real numbers}
 and
{x : x = (0, 2, 1) + t(1, 0, 2), t is in the set of real numbers}.

    

θ =


(iv) The line through (−1, 4, 1) with direction vector (3, −1, 2) and
{(x, y, z) : x = 2t, y = 3 − 2t, z = 3 + 4t, t is in the set of real numbers}.

    

θ =
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5. –/3 points DamianoMVCalc1 1.4.009. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
Determine if the following pairs of lines are orthogonal.
(a) The line through P = (1, 0, −3) with direction vector (−1, 2, 1) and the line through Q = (0, 3, 1) with direction vector (2, 1, −1).
    

(b) The line through P = (−1, 3, 2) with direction vector (0, −2, −2) and the line through Q = (0, 2, 1) with direction vector (2, 1, −1).
    

(c) The line through P = (2, 1, 2) with direction vector (−1, 2, 1) and the line through Q = (0, 5, 4) with direction vector (1, 1, −1).
    
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6. –/4 points DamianoMVCalc1 1.4.011. My Notes
Question Part
Points
Submissions Used
1 2 3 4
–/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50
Total
–/4
 
Find a coordinate equation for each of the planes described below. (Use x, y, and z for coordinates.)
(a) The plane containing the point P = (1, −1, 2) with normal vector n = (1, 0, 1).


(b) The plane containing the point P = (4, 1, −1) with normal vector n = (−1, 2, 1).


(c) The plane containing the point P = (1, 1, 2) and the vectors u = (1, −1, 1) and v = (0, 2, −2).


(d) The plane containing the points P = (1, 0, 2), Q = (−2, 3, 2), and R = (1, −1, 0).
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7. –/6 points DamianoMVCalc1 1.4.013. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
–/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50
Total
–/6
 
For each of the following, determine if the point Q is on the plane. If not, find the distance from the point Q to the plane. (If the point is on the plane, enter 0 for the distance.)
(a) The plane is given by the equation
2x − y + 3z = 8
 and the point Q = (3, 2, −1).
    

The distance is
.

(b) The plane is given by the equation
4x − y + 3z = 6
 and the point Q = (1, 1, 1).
    

The distance is
.

(c) The plane is given by the equation
x + y − 2z = 2
 and the point Q = (1, 2, −1).
    

The distance is
.
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