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Marsden and Tromba - Vector Calculus 6/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 2 / 33

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
1/1 0/1 1/3 –/4 –/1 –/20 –/3
Total
2/33 (6.1%)

  • Instructions

    Vector Calculus, 6th edition, by Jerrold E. Marsden and Anthony Tromba and published by W.H. Freeman, helps students gain an intuitive and solid understanding of calculus. The book's careful account is a contemporary balance between theory, application, and historical development, providing its readers with an insight into how mathematics progresses and is in turn influenced by the natural world. The WebAssign component for this title offers students immediate feedback on randomized questions straight from the textbook as well as access to an eBook.

    Questions 1 and 5 feature grading for a parametrized vector and parametric equations, respectively. Try entering different parametrizations!

    Question 2 utilizes list grading to accept both solutions of the problem in any order.

    Question 3 demonstrates standard vector grading that allows the vector to be entered either in component form or in terms of i and j.

    Question 4 contains standard equation grading, which accepts any equivalent equation as correct.

    Question 6 deals with rectangular, cylindrical, and spherical ordered triples, and each component can be written in a variety of ways.

    Question 7 shows vector grading that allows only positive scalar multiples of the vectors to indicate the desired direction. 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.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

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1. 1/1 points  |  Previous Answers MarsVectorCalc6 1.1.013. My Notes
Question Part
Points
Submissions Used
1
1/1
3/100
Total
1/1
 
Use vector notation to describe the points that lie in the given configuration. (Let s and t be elements of the Reals.)
the plane spanned by
v1 = (2, 8, 0)
 and
v2 = (0, 2, 8)
l(s, t) =
(2s,8s+2t,8t)
Correct: Your answer is correct. webMathematica generated answer key
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2. 0/1 points  |  Previous Answers MarsVectorCalc6 1.2.019. My Notes
Question Part
Points
Submissions Used
1
0/1
3/100
Total
0/1
 
Find all values of x such that
(4, x, −12)
 and
(8, x, x)
 are orthogonal. (Enter your answers as a comma-separated list.)
x =
√3211​
Incorrect: Your answer is incorrect. webMathematica generated answer key
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3. 1/3 points  |  Previous Answers MarsVectorCalc6 1.2.037. My Notes
Question Part
Points
Submissions Used
1 2 3
0/1 1/1 0/1
1/100 2/100 1/100
Total
1/3
 
A force of 4 N makes an angle of
π
4
 radian
 with the y-axis, pointing to the right. The force acts against the movement of an object along the straight line connecting
(4, 2)
 to
(5, 4).
(a)
Find a formula for the force vector F.
F =
2√2i+2√2j
Incorrect: Your answer is incorrect. webMathematica generated answer key
(b)
Find the angle θ between the displacement direction
D = (5 − 4)i + (4 − 2)j
 and the force direction F. (Round your answer to one decimal place.)
θ = Correct: Your answer is correct. seenKey

18.4

 °
(c)
The work done is
F · D,
 or, equivalently,
F
D
 cos(θ).
 Compute the work from both formulas and compare.
8.5
Incorrect: Your answer is incorrect. webMathematica generated answer key N

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4. –/4 points MarsVectorCalc6 1.3.015. My Notes
Question Part
Points
Submissions Used
1 2 3 4
–/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100
Total
–/4
 
(a)
Find an equation for the plane that is perpendicular to
v = (1, 1, 1)
 and passes through
(1, 0, 0).
(b)
Find an equation for the plane that is perpendicular to
v = (1, 3, 7)
 and passes through
(1, 1, 1).
(c)
Find an equation for the plane that is perpendicular to the line
l(t) = (2, 0, 5)t + (4, −1, 1)
 and passes through
(2, −1, 0).
(d)
Find an equation for the plane that is perpendicular to the line
l(t) = (−3, −4, 8)t + (0, 5, 1)
 and passes through
(5, 2, −1).

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5. –/1 points MarsVectorCalc6 1.3.021. My Notes
Question Part
Points
Submissions Used
1
–/1
0/100
Total
–/1
 
Find the parametric equations of the intersection of the planes
x + (y − 2) + z = 0
 and
−x + (y + 2) − z = 0.
 (Use the parameter t. Enter your answers as a comma-separated list of equations.)
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6. –/20 points MarsVectorCalc6 1.4.003. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
–/20
 
(a)
The following points are given in cylindrical coordinates; express each in rectangular coordinates and spherical coordinates.
Cylindrical
(r, θ, z)
 		Rectangular
(x, y, z)
 		Spherical
(ρ, θ, ϕ)
(1, 45°, 4)
3, 
π
2
, −4
(0, 45°, 12)
5, 
π
6
, 12
1, 
π
6
, 0
2, 
3π
4
, −2
(b)
Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.
Rectangular
(x, y, z)
 		Spherical
(ρ, θ, ϕ)
 		Cylindrical
(r, θ, z)
(4, 2, −4)
(0, 8, 15),
(
2
, 1, 1)
(−2
3
, −2, 3)

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7. –/3 points MarsVectorCalc6 2.6.011. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/100 0/100 0/100
Total
–/3
 
For the functions below, what is the direction of fastest increase at
(1, 1, 1)?
(a)
f(x, y, z) = 
1
x2 + y2 + z2
(b)
f(x, y, z) = 8xy + 8yz + 8xz
(c)
f(x, y, z) = 
2
x2 + y2 + z2
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