100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
MAT1503 ASSIGNMENT 7 2021 $8.53   Add to cart
Quickly navigate to
Preview
  2.  
  3. University Of South Africa (Unisa)
  4.  
  5. MAT1503 - Linear Algebra (MAT1503)

Other

MAT1503 ASSIGNMENT 7 2021

1 review
 50 views  11 purchases
  • Course
  • MAT1503 - Linear Algebra (MAT1503)
  • Institution
  • University Of South Africa (Unisa)

This document contains solutions of MAT1503 ASSIGNMENT 7 2021 .All workings are shown and explanations are provided.Please note that there is no question 5.2 because there is a mistake on the question.

Preview 2 out of 9  pages

Document information

  • July 11, 2021
  • 9
  • 2021/2022
  • Other
  • Unknown

Subjects

  • mat1503
  • linear algebra
  • gimmenotes
  • stuvia
  • google
  • unisa

Written for

  • University of South Africa (Unisa)
  • MAT1503 - Linear Algebra (MAT1503)
All documents for this subject (136)

1  review

review-writer-avatar

By: patuxolom • 3 year ago

Seller

avatar-seller
jctutor0814378595

Reviews received

Content preview

MAT1503


ASSIGNMENT 7 2021



QUESTION 1


QUESTION 1.1


a).


𝑥 = 1 + 𝑡 , 𝑦 = −1 − 𝑡 , 𝑧 = −2𝑡

(𝑥, 𝑦, 𝑧) = (1 + 𝑡 , −1 − 𝑡 , −2𝑡)

(𝑥, 𝑦, 𝑧) = (1, −1,0) + 𝑡(1, −1, −2)

𝐿𝑒𝑡 ∶ 𝑣⃗ = 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑣𝑒𝑐𝑡𝑜𝑟 𝑜𝑓 𝑙𝑖𝑛𝑒 = (1, −1, −2)

𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑝𝑙𝑎𝑛𝑒 ∶ 𝑥 + 2𝑦 + 3𝑧 − 9 = 0

𝑛⃗⃗ = 𝑛𝑜𝑟𝑚𝑎𝑙 𝑜𝑓 𝑝𝑙𝑎𝑛𝑒

𝑛⃗⃗ = (1,2,3)

𝑛⃗⃗ ∙ 𝑣⃗ = (1,2,3) ∙ (1, −1, −2)

=1−2−6

= −7

𝑆𝑖𝑛𝑐𝑒 𝑛⃗⃗ ∙ 𝑣⃗ ≠ 0 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑙𝑖𝑛𝑒 𝑎𝑛𝑑 𝑝𝑙𝑎𝑛𝑒 𝑎𝑟𝑒 𝑛𝑜𝑡 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙.

, b).


𝐿𝑒𝑡 ∶ 𝑣⃗ = 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑣𝑒𝑐𝑡𝑜𝑟 𝑜𝑓 𝑙𝑖𝑛𝑒 = (3,2, −1)

𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑝𝑙𝑎𝑛𝑒 ∶ 4𝑥 − 𝑦 + 2𝑧 + 1 = 0

𝑛⃗⃗ = 𝑛𝑜𝑟𝑚𝑎𝑙 𝑜𝑓 𝑝𝑙𝑎𝑛𝑒

𝑛⃗⃗ = (4, −1,2)

𝑛⃗⃗ ∙ 𝑣⃗ = (4, −1,2) ∙ (3,2, −1)

= 12 − 2 − 2

=8



𝑆𝑖𝑛𝑐𝑒 𝑛⃗⃗ ∙ 𝑣⃗ ≠ 0 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑙𝑖𝑛𝑒 𝑎𝑛𝑑 𝑝𝑙𝑎𝑛𝑒 𝑎𝑟𝑒 𝑛𝑜𝑡 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙.




QUESTION 2


QUESTION 2.1


𝑃 = (2,0, −1) , 𝑛⃗⃗ = 〈2,1,3〉

𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑙𝑖𝑛𝑒: 𝑟 = 𝑟𝑜 + 𝑡𝑣

𝑟 = 〈𝑥, 𝑦, 𝑧〉 = 𝑔𝑒𝑛𝑒𝑟𝑎𝑙 𝑝𝑜𝑖𝑛𝑡

𝑟𝑜 = 𝑝𝑜𝑖𝑛𝑡 𝑡ℎ𝑎𝑡 𝑙𝑖𝑒𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑙𝑖𝑛𝑒 = 〈2,0, −1〉

𝑣 = 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑣𝑒𝑐𝑡𝑜𝑟 𝑜𝑓 𝑙𝑖𝑛𝑒 = 𝑛⃗⃗

𝑣 = 〈2,1,3〉

〈𝑥, 𝑦, 𝑧〉 = 〈2,0, −1〉 + 𝑡〈2,1,3〉

〈𝑥, 𝑦, 𝑧〉 = 〈2 + 2𝑡 , 𝑡 , −1 + 3𝑡〉

𝑃𝑎𝑟𝑎𝑚𝑒𝑡𝑟𝑖𝑐 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛:

𝑥 = 2 + 2𝑡 , 𝑦 = 𝑡 , 𝑧 = −1 + 3𝑡

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller jctutor0814378595. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $8.53. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

75057 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$8.53  11x  sold
  • (1)
  Add to cart