Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Related questions
Question
Please help me with this. Please check if I've gotten the write answer for each questions. And if I have shown the correct steps. Just check question c), d) and e)
Just write the answers that are correct (e.g. a) correct, b) incorrect )
Image 1: The question
Image 2: My work
Transcribed Image Text:Suppose vector i = [-3,4,-6) and originates at point A at (1,5,-3) and terminates at point B at (3,6,9)
a. Find vector and write it in both ordered pair and unit vector notation
b. Find a normal to vectors and
c. Find a unit vector that is the same magnitude as the normal you obtained in question 2, part b.
Use the dot product to verify that the normal you obtained in question 2, part b is orthogonal to
both vectors and
d.
e. Suppose vectors and are both direction vectors in a plane that also contains the point
(2,-4,7). Determine:
L
A vector equation for the plane
Parametric equations for the plane
A scalar equation for the plane
![Given that U: [-3, 4, -6] Point A [1, 5,-3] point B[3,6,9]
V = [ 3-1, 6-5, 9 +(-3)]
V = [2, 1, 12]
This helped
a) So, V₁ = [2, 1, 12],
J = 2₁ + J + 12^1 (unit vector notation) Verifying ʼn is orthogonal tou
R
b) n = √₂ x v
R=
A
J
ĴK
4
-3
2
77² = 1 (48 + 6)-Ĵ(-36 +12) + K (-3-8)
54₁ +24 ^j - 11 k
-6
1 12
1
d)
(ordered pair notation) (using part b)
c)
Let w = 541 + 241-11 K
J (54)² + (24)² + (-11) ²
= 541 + 24 7 - HK
√2916 +576 + 121
4
= 54 ↑ + 24 Ĵ-11 k
J3613
√3613
OR
(54î+24ĵ-11K)
34
54 7 + 24 J
03613 J3613
11
√3613
K
n⋅U = [54, 24, -11], (-3, 4, -6]
= -162 +96-66
= 0
Verifying
in is orthogonal to V
R⋅V = [54₁ 24₁ -11]. [2, 1, 12]
= 108 + 24 =132
=0
e) Planc contains (2, +4,7)
normal (n) = [54, 24, -11]
Vector Equation
[R-(21-4j+ 7^k)]. [54^₁ + 24 ²5 -11 K ] = 0
Parametric, equation
U= [-3₁4₁-6]
V = [2/1, 12]
x = 2-3 £1+ 2+₂
y = - 4 +4€₂+ €₂
2= 7 -6 €₁ + 12 € ₂
Scalar Equation
54 (x-2) ₁24 (y + 4) - 11 (2-7)= 0
54x + 24 y = 11² + 65 =0
(-](https://content.bartleby.com/qna-images/question/f53b1b3a-ce83-4673-9838-32a83916512b/6c25f7e6-5fdf-401e-b742-3be285797d38/th0ygrs_processed.jpeg)
Transcribed Image Text:Given that U: [-3, 4, -6] Point A [1, 5,-3] point B[3,6,9]
V = [ 3-1, 6-5, 9 +(-3)]
V = [2, 1, 12]
This helped
a) So, V₁ = [2, 1, 12],
J = 2₁ + J + 12^1 (unit vector notation) Verifying ʼn is orthogonal tou
R
b) n = √₂ x v
R=
A
J
ĴK
4
-3
2
77² = 1 (48 + 6)-Ĵ(-36 +12) + K (-3-8)
54₁ +24 ^j - 11 k
-6
1 12
1
d)
(ordered pair notation) (using part b)
c)
Let w = 541 + 241-11 K
J (54)² + (24)² + (-11) ²
= 541 + 24 7 - HK
√2916 +576 + 121
4
= 54 ↑ + 24 Ĵ-11 k
J3613
√3613
OR
(54î+24ĵ-11K)
34
54 7 + 24 J
03613 J3613
11
√3613
K
n⋅U = [54, 24, -11], (-3, 4, -6]
= -162 +96-66
= 0
Verifying
in is orthogonal to V
R⋅V = [54₁ 24₁ -11]. [2, 1, 12]
= 108 + 24 =132
=0
e) Planc contains (2, +4,7)
normal (n) = [54, 24, -11]
Vector Equation
[R-(21-4j+ 7^k)]. [54^₁ + 24 ²5 -11 K ] = 0
Parametric, equation
U= [-3₁4₁-6]
V = [2/1, 12]
x = 2-3 £1+ 2+₂
y = - 4 +4€₂+ €₂
2= 7 -6 €₁ + 12 € ₂
Scalar Equation
54 (x-2) ₁24 (y + 4) - 11 (2-7)= 0
54x + 24 y = 11² + 65 =0
(-
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 3 steps with 47 images
Knowledge Booster
Similar questions
- Directions: Prepare, or complete, a flowchart proof and a two-column proof for the following problems. Given: AE and BD bisect each other 1. Prove: AABC = AEDC E Flowchart Proof: Two-column Proof: Statements Reasons All Rights Reserved © MathBits.comarrow_forwardMatch these values of r with the accompanying scatterplots: 0.402, 0.736, -0.736, -1, and 1. Click the icon to view the scatterplots. Match the values of r to the scatterplots. Scatterplot 1, r= Scatterplot 2, r= Scatterplot 3, r= Scatterplot 4, r = Scatterplot 5, r = V ▼ Scatterplots 15- 14- 13- 12- 11- 10+ 0 8- 6- 4. 2- 0- 0 4 Scatterplot 1 . • 0.2 0.4 0.6 0.8 1 x Scatterplot 4 0.2 0.4 0.6 0.8 x • 1 Q Q Q ✔ 8 6- > 4- 2 ▬▬▬▬▬▬▬▬▬▬o 0- 0 0.2 0.4 0.6 0.8 -14 Scatterplot 2 0 • X Scatterplot 5 1 0.2 0.4 0.6 0.8 1 C Q Q ✔ Q Q > 8- 6- 4- 2 0- 0 0 · Scatterp T 0.2 0.4 0.6 X ▶ Xarrow_forwardINSTRUCTIONS: For the assignment below, prepare answers in a Word document (.doc or .docx) and submit a single file to the Dropbox. You should use Excel to calculate your answers, and be sure to submit both your calculations and final answers. Calculations can be pasted from Excel into your Word document. Note that Excel calculations are supporting documentation, but you still need to explain the exact answers in narrative form in order to receive full credit. In addition to the textbook, check out the Unit 5 Resources section for additional content including PowerPoints and video tutorials that might aid you in your calculations. You can find a "case study template" to use under Course Home. Remember to include a title page, introduction, conclusion, and reference list. See further below for grading rubric. NOTE: You will need to access the 'Analysis Toolpak' in Excel in order to perform the calculations for this case. If you have not already installed this free add-in, please…arrow_forward
- bard.com Question Completion Status: QUESTION 3 Which of the following relations are functions where y is a function of x? A. B. Click Save and Submit to stue hid si bmit. Click Save All Answers to save all answers. Sa ch F2 F3 F4 FSarrow_forwardInstruction: The given problem below has been solved for you. Your job is to check the answers for errors. If there are errors, do the following in the given table. a. Review each step of the problem. b. Determined whether the given step is correct or if there is an error. c. If a particular step has an error, explain it and make necessary correction. d. Explain the correction. Tata is working as a city Engineer. The city mayor asks him to propose an irregular shape playground design. Aside from this, the mayor wanted the playground to be covered with frog grass. How much budget the Mayor should allocate to cover the entire park with frog grass? OTHER STEPS INCLUDEDSTEP 3:Region 1: Solve the shaded region between f(x)=-x^2/100+200 and g(x)=0bounded from x=0 to x=200.Region 2: Solve the shaded region between f(x)=-x^2/100+200 and g(x)=0bounded from x=0 to x=100.Region 3: Solve the shaded region between h(x)=x and g(x)=0 bounded from x=0 to x=141.24. Step 8: Solve for the allocated…arrow_forwardName: Ill Teacher: Ms. Cahill / Mrs. Helmsing 3.2.1 Practice a. 6-721 Student Schedule For Harris, Izabella A Student Number: 18696 3-34. The number 6 is represented with+ and tiles at right. For each problem below, start with this diagram and then show how to remove the appropriate number of tiles to represent the problem given. State the final answer for each part. ++++ Block: 4/5 +++arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
Numerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat...Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY 
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Advanced Engineering Mathematics
Advanced Math
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:9780073397924
Author:Steven C. Chapra Dr., Raymond P. Canale
Publisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat...
Advanced Math
ISBN:9781118141809
Author:Nathan Klingbeil
Publisher:WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,