exam elaboration mat1503_assignment_6_2021 MAT1503 ASSIGNMENT 6 2021

MAT1503 ASSIGNMENT 6 2021

written by

jctutor0814378595




www.stuvia.com




Downloaded by: mkhaliphit |
Distribution of this document is illegal

, Stuvia.com - The Marketplace to Buy and Sell your Study Material




MAT1503


ASSIGNMENT 6 2021


QUESTION 1


QUESTION 1.1


⃗ = 〈1,3, −2〉 𝑎𝑛𝑑 𝑣 = 〈−5,3,2〉
𝑢

𝐿𝑒𝑡 𝑡ℎ𝑒 𝑎𝑛𝑙𝑔𝑙𝑒 = 𝜃

𝑢⃗ ∙𝑣
cos(𝜃) =
‖𝑢
⃗ ‖‖𝑣‖

⃗ ∙ 𝑣 = 〈1,3, −2〉 ∙ 〈−5,3,2〉
𝑢

𝑢
⃗ ∙ 𝑣 = −5 + 9 − 4 = 0

𝑆𝑖𝑛𝑐𝑒 𝑢
⃗ ∙ 𝑣 = 0 𝑡ℎ𝑒𝑛 𝑢
⃗ 𝑎𝑛𝑑 𝑣 𝑎𝑟𝑒 𝑜𝑟𝑡ℎ𝑜𝑔𝑜𝑛𝑎𝑙 𝑣𝑒𝑐𝑡𝑜𝑟𝑠



QUESTION 1.2


⃗ = 〈1, −2,4〉 𝑎𝑛𝑑 𝑣 = 〈5,3,7〉
𝑢

𝐿𝑒𝑡 𝑡ℎ𝑒 𝑎𝑛𝑙𝑔𝑙𝑒 = 𝜃

𝑢⃗ ∙𝑣
cos(𝜃) =
‖𝑢
⃗ ‖‖𝑣‖

⃗ ∙ 𝑣 = 〈1, −2,4〉 ∙ 〈5,3,7〉
𝑢

= 5 − 6 + 28

= 27

⃗ ‖ = √(1)2 + (−2)2 + (4)2 = √21
‖𝑢

‖𝑣 ‖ = √(5)2 + (3)2 + (2)2 = √38



27
cos(𝜃) =
√21 ∙ √38



Downloaded by: mkhaliphit |
Distribution of this document is illegal

, Stuvia.com - The Marketplace to Buy and Sell your Study Material




27
𝜃 = cos−1 ( )
√21 ∙ √38

𝜃 = 17.1° 𝑡ℎ𝑒 𝑎𝑛𝑔𝑙𝑒 𝑖𝑠 𝑎𝑛 𝑎𝑐𝑢𝑡𝑒




QUESTION 2


QUESTION 2.1


𝑎∙𝑢⃗
𝑝𝑟𝑜𝑎 𝑢
⃗ = 𝑎
|𝑎|2

𝑎 = 〈−1, −3〉

|𝑎| = √(−1)2 + (−3)2 = √10

⃗ = 〈−1,3〉
𝑢

〈−1, −3〉 ∙ 〈−1,3〉
𝑝𝑟𝑜𝑎 𝑢
⃗ = 2
〈−1, −3〉
(√10)

1−9
= 〈−1, −3〉
10
8
=− 〈−1, −3〉
10
4
= − 〈−1, −3〉
5
4 12
=〈 , 〉
5 5
4 12
⃗ =〈 , 〉
𝑝𝑟𝑜𝑎 𝑢
5 5




QUESTION 2.2


𝑎∙𝑢 ⃗
𝑝𝑟𝑜𝑎 𝑢
⃗ = 2
𝑎
|𝑎|




Downloaded by: mkhaliphit |
Distribution of this document is illegal