ºÝºÝߣ

ºÝºÝߣShare a Scribd company logo
Exercise -1(A) : If r = sinti = costj = tk, find
(i)
??
??
(ii)
?2
?
??2 (iii)|
??
??
| (iv)|
?2
?
??2 |
Solution : (i)
??
??
=
?
??
(sinti = costj = tk)
= costi-sinti+tk
(ii)
?2
?
??2 =
??
??
{
??
??
(sinti + costj + tk)}
??
??
(cosi - sintj + tk)
=-sinti-costj
(iii)
??
??
= cosi + sintj + tk
|
??
??
| = ¡Ì???2 ? + ???? ? + 12 = ¡Ì1 + 1 = ¡Ì2
(iv) |
?2
?
??2 |=¡Ì???2 ? + ???2 ? = ¡Ì1 = 1
Solution : Let ¨Cr,be the position vector of the particle at any time t.
R=xi+yj+zk
=???
? + 2???3?? + 2???3??
V=
??
??
=
?
??
(???
+ 2???3?? + 2???3??)
=???
? ? 6???3?? + 6???3??
? =
?2
?
??2
=
?
??
(????
? ? 6???3?? + 6???3??)
=???
? ? 18???3?? ? 18???3?? t=0,
At t=0,
V=-i+6k
| ?| = ¡Ì?12 + 62 = ¡Ì37
At t= 0, a= i-18 cos 0.j-18 sin 3.0k
=i-0-18
| ?|= ¡Ì(1)2 + (?18)2 = ¡Ì1 + 324 = ¡Ì325
a book
Ad

Recommended

Discrete Mathematical Structures - Fundamentals of Logic - Principle of duality
Discrete Mathematical Structures - Fundamentals of Logic - Principle of duality
Lakshmi R
?
Rabin Karp Algorithm
Rabin Karp Algorithm
Kiran K
?
Bohmian
Bohmian
Reece Boston
?
Quantum Machine Learning and QEM for Gaussian mixture models (Alessandro Luongo)
Quantum Machine Learning and QEM for Gaussian mixture models (Alessandro Luongo)
MeetupDataScienceRoma
?
Rules of Derivative
Rules of Derivative
Alishba Saeed
?
Logical equivalence, laws of logic
Logical equivalence, laws of logic
Lakshmi R
?
Naive string matching algorithm
Naive string matching algorithm
Kiran K
?
Linear sort
Linear sort
Amit Kumar Rathi
?
English math - where should a pilot start descent
English math - where should a pilot start descent
Visca Amelia S
?
Summing the squares of a number's digits
Summing the squares of a number's digits
goldenratio618
?
Discretization
Discretization
NARESH MEENA
?
Prim algorithm
Prim algorithm
University of Potsdam
?
Variational AutoEncoder
Variational AutoEncoder
Kazuki Nitta
?
Cayley-Hamilton Theorem, Eigenvalues, Eigenvectors and Eigenspace.
Cayley-Hamilton Theorem, Eigenvalues, Eigenvectors and Eigenspace.
Isaac Yowetu
?
Linear regression with one variable
Linear regression with one variable
klchou
?
È·ÂʵÄÍÆÂÛ¤ÈÐж¯Ñ¡’k
È·ÂʵÄÍÆÂÛ¤ÈÐж¯Ñ¡’k
Masahiro Suzuki
?
Question 1c Math 1
Question 1c Math 1
M.T.H Group
?
Complexity Classes and the Graph Isomorphism Problem
Complexity Classes and the Graph Isomorphism Problem
cseiitgn
?
Éî²ãÉú³É¥â¥Ç¥ë¤òÓ䤤¿¥Þ¥ë¥Á¥â©`¥À¥ë¥Ç©`¥¿¤Î°ë½Ìʦ¤¢¤êѧϰ
Éî²ãÉú³É¥â¥Ç¥ë¤òÓ䤤¿¥Þ¥ë¥Á¥â©`¥À¥ë¥Ç©`¥¿¤Î°ë½Ìʦ¤¢¤êѧϰ
Masahiro Suzuki
?
¡¾DL݆Õi»á¡¿NeRF-VAE: A Geometry Aware 3D Scene Generative Model
¡¾DL݆Õi»á¡¿NeRF-VAE: A Geometry Aware 3D Scene Generative Model
Deep Learning JP
?
Paper Review: An exact mapping between the Variational Renormalization Group ...
Paper Review: An exact mapping between the Variational Renormalization Group ...
Kai-Wen Zhao
?
Ch06 6
Ch06 6
Rendy Robert
?
°Ú¶Ù³¢ÂÖÕi»á±Õ³Ò´¡±·¤È¥¨¥Í¥ë¥®©`¥Ù©`¥¹¥â¥Ç¥ë
°Ú¶Ù³¢ÂÖÕi»á±Õ³Ò´¡±·¤È¥¨¥Í¥ë¥®©`¥Ù©`¥¹¥â¥Ç¥ë
Deep Learning JP
?
[DL݆Õi»á]The Cramer Distance as a Solution to Biased Wasserstein Gradients
[DL݆Õi»á]The Cramer Distance as a Solution to Biased Wasserstein Gradients
Deep Learning JP
?
Improved Trainings of Wasserstein GANs (WGAN-GP)
Improved Trainings of Wasserstein GANs (WGAN-GP)
Sangwoo Mo
?
Recursive Compressed Sensing
Recursive Compressed Sensing
Pantelis Sopasakis
?
Truth, deduction, computation lecture i (last one)
Truth, deduction, computation lecture i (last one)
Vlad Patryshev
?
Projectors and Projection Onto a Line
Projectors and Projection Onto a Line
Isaac Yowetu
?
Z writing for the professions pdf 1
Z writing for the professions pdf 1
macee94
?
O2 Holiday Collection
O2 Holiday Collection
Kimberly Spencer
?

More Related Content

What's hot (20)

English math - where should a pilot start descent
English math - where should a pilot start descent
Visca Amelia S
?
Summing the squares of a number's digits
Summing the squares of a number's digits
goldenratio618
?
Discretization
Discretization
NARESH MEENA
?
Prim algorithm
Prim algorithm
University of Potsdam
?
Variational AutoEncoder
Variational AutoEncoder
Kazuki Nitta
?
Cayley-Hamilton Theorem, Eigenvalues, Eigenvectors and Eigenspace.
Cayley-Hamilton Theorem, Eigenvalues, Eigenvectors and Eigenspace.
Isaac Yowetu
?
Linear regression with one variable
Linear regression with one variable
klchou
?
È·ÂʵÄÍÆÂÛ¤ÈÐж¯Ñ¡’k
È·ÂʵÄÍÆÂÛ¤ÈÐж¯Ñ¡’k
Masahiro Suzuki
?
Question 1c Math 1
Question 1c Math 1
M.T.H Group
?
Complexity Classes and the Graph Isomorphism Problem
Complexity Classes and the Graph Isomorphism Problem
cseiitgn
?
Éî²ãÉú³É¥â¥Ç¥ë¤òÓ䤤¿¥Þ¥ë¥Á¥â©`¥À¥ë¥Ç©`¥¿¤Î°ë½Ìʦ¤¢¤êѧϰ
Éî²ãÉú³É¥â¥Ç¥ë¤òÓ䤤¿¥Þ¥ë¥Á¥â©`¥À¥ë¥Ç©`¥¿¤Î°ë½Ìʦ¤¢¤êѧϰ
Masahiro Suzuki
?
¡¾DL݆Õi»á¡¿NeRF-VAE: A Geometry Aware 3D Scene Generative Model
¡¾DL݆Õi»á¡¿NeRF-VAE: A Geometry Aware 3D Scene Generative Model
Deep Learning JP
?
Paper Review: An exact mapping between the Variational Renormalization Group ...
Paper Review: An exact mapping between the Variational Renormalization Group ...
Kai-Wen Zhao
?
Ch06 6
Ch06 6
Rendy Robert
?
°Ú¶Ù³¢ÂÖÕi»á±Õ³Ò´¡±·¤È¥¨¥Í¥ë¥®©`¥Ù©`¥¹¥â¥Ç¥ë
°Ú¶Ù³¢ÂÖÕi»á±Õ³Ò´¡±·¤È¥¨¥Í¥ë¥®©`¥Ù©`¥¹¥â¥Ç¥ë
Deep Learning JP
?
[DL݆Õi»á]The Cramer Distance as a Solution to Biased Wasserstein Gradients
[DL݆Õi»á]The Cramer Distance as a Solution to Biased Wasserstein Gradients
Deep Learning JP
?
Improved Trainings of Wasserstein GANs (WGAN-GP)
Improved Trainings of Wasserstein GANs (WGAN-GP)
Sangwoo Mo
?
Recursive Compressed Sensing
Recursive Compressed Sensing
Pantelis Sopasakis
?
Truth, deduction, computation lecture i (last one)
Truth, deduction, computation lecture i (last one)
Vlad Patryshev
?
Projectors and Projection Onto a Line
Projectors and Projection Onto a Line
Isaac Yowetu
?
English math - where should a pilot start descent
English math - where should a pilot start descent
Visca Amelia S
?
Summing the squares of a number's digits
Summing the squares of a number's digits
goldenratio618
?
Variational AutoEncoder
Variational AutoEncoder
Kazuki Nitta
?
Cayley-Hamilton Theorem, Eigenvalues, Eigenvectors and Eigenspace.
Cayley-Hamilton Theorem, Eigenvalues, Eigenvectors and Eigenspace.
Isaac Yowetu
?
Linear regression with one variable
Linear regression with one variable
klchou
?
È·ÂʵÄÍÆÂÛ¤ÈÐж¯Ñ¡’k
È·ÂʵÄÍÆÂÛ¤ÈÐж¯Ñ¡’k
Masahiro Suzuki
?
Complexity Classes and the Graph Isomorphism Problem
Complexity Classes and the Graph Isomorphism Problem
cseiitgn
?
Éî²ãÉú³É¥â¥Ç¥ë¤òÓ䤤¿¥Þ¥ë¥Á¥â©`¥À¥ë¥Ç©`¥¿¤Î°ë½Ìʦ¤¢¤êѧϰ
Éî²ãÉú³É¥â¥Ç¥ë¤òÓ䤤¿¥Þ¥ë¥Á¥â©`¥À¥ë¥Ç©`¥¿¤Î°ë½Ìʦ¤¢¤êѧϰ
Masahiro Suzuki
?
¡¾DL݆Õi»á¡¿NeRF-VAE: A Geometry Aware 3D Scene Generative Model
¡¾DL݆Õi»á¡¿NeRF-VAE: A Geometry Aware 3D Scene Generative Model
Deep Learning JP
?
Paper Review: An exact mapping between the Variational Renormalization Group ...
Paper Review: An exact mapping between the Variational Renormalization Group ...
Kai-Wen Zhao
?
°Ú¶Ù³¢ÂÖÕi»á±Õ³Ò´¡±·¤È¥¨¥Í¥ë¥®©`¥Ù©`¥¹¥â¥Ç¥ë
°Ú¶Ù³¢ÂÖÕi»á±Õ³Ò´¡±·¤È¥¨¥Í¥ë¥®©`¥Ù©`¥¹¥â¥Ç¥ë
Deep Learning JP
?
[DL݆Õi»á]The Cramer Distance as a Solution to Biased Wasserstein Gradients
[DL݆Õi»á]The Cramer Distance as a Solution to Biased Wasserstein Gradients
Deep Learning JP
?
Improved Trainings of Wasserstein GANs (WGAN-GP)
Improved Trainings of Wasserstein GANs (WGAN-GP)
Sangwoo Mo
?
Truth, deduction, computation lecture i (last one)
Truth, deduction, computation lecture i (last one)
Vlad Patryshev
?
Projectors and Projection Onto a Line
Projectors and Projection Onto a Line
Isaac Yowetu
?

Viewers also liked (12)

Z writing for the professions pdf 1
Z writing for the professions pdf 1
macee94
?
O2 Holiday Collection
O2 Holiday Collection
Kimberly Spencer
?
?????????????????????
?????????????????????
pyopyo
?
Live nhra thunder valley nationals on web
Live nhra thunder valley nationals on web
austinben137
?
Duncan & Toplis Directors' Briefing: Peter Watson
Duncan & Toplis Directors' Briefing: Peter Watson
Bradley McKenny
?
bachelor in nursing (leadership and management)
bachelor in nursing (leadership and management)
Shristi Aryal
?
Housing
Housing
Ahmed Ameen
?
Industrial Lighting
Industrial Lighting
Gagan Tanwar
?
Scavenger Hunt
Scavenger Hunt
midrausbiggers
?
Hiv aids
Hiv aids
carlyrelf
?
Cigarette adverts
Cigarette adverts
carlyrelf
?
Defining Affordable Housing in Nigeria. v2.2.sg01.07.16
Defining Affordable Housing in Nigeria. v2.2.sg01.07.16
Simon Gusah MPIA, ANIA
?
Z writing for the professions pdf 1
Z writing for the professions pdf 1
macee94
?
?????????????????????
?????????????????????
pyopyo
?
Live nhra thunder valley nationals on web
Live nhra thunder valley nationals on web
austinben137
?
Duncan & Toplis Directors' Briefing: Peter Watson
Duncan & Toplis Directors' Briefing: Peter Watson
Bradley McKenny
?
bachelor in nursing (leadership and management)
bachelor in nursing (leadership and management)
Shristi Aryal
?
Cigarette adverts
Cigarette adverts
carlyrelf
?
Defining Affordable Housing in Nigeria. v2.2.sg01.07.16
Defining Affordable Housing in Nigeria. v2.2.sg01.07.16
Simon Gusah MPIA, ANIA
?
Ad

Recently uploaded (20)

The Future State Of Work - Actionable Summary for Startup Founders
The Future State Of Work - Actionable Summary for Startup Founders
vikram sood
?
Improving Sales Forecasting in Volatile B2B Capital Equipment Markets - Dave ...
Improving Sales Forecasting in Volatile B2B Capital Equipment Markets - Dave ...
Dave Litwiller
?
Enterprise Architecture Professional Journal Vol IX June 2025.pdf
Enterprise Architecture Professional Journal Vol IX June 2025.pdf
Darryl_Carr
?
Filter Test machine .pdf
Filter Test machine .pdf
FILTRATION ENGINEERING & CUNSULTANT
?
StarOps- AI-native platform that lets you deploy and manage production infras...
StarOps- AI-native platform that lets you deploy and manage production infras...
StarOps
?
Electronic Shelf Labels & Digital Price Tags in Delhi | Foodcare
Electronic Shelf Labels & Digital Price Tags in Delhi | Foodcare
Foodcare llp
?
Essar at IEW 2025, Leading the Way to India¡¯s Green Energy Transition.
Essar at IEW 2025, Leading the Way to India¡¯s Green Energy Transition.
essarcase
?
Hire the Best Crypto Recovery Experts for Fast Recovery in 2025: Puran Crypto...
Hire the Best Crypto Recovery Experts for Fast Recovery in 2025: Puran Crypto...
henryywalker3
?
placement-brochure Great lakes Gurgaon. 2025
placement-brochure Great lakes Gurgaon. 2025
charankumarboom
?
The Science Behind Effective Lead Nurture Programs in B2B Marketing.pptx
The Science Behind Effective Lead Nurture Programs in B2B Marketing.pptx
brandonsoros91
?
Rushi Manche | Blockchain Tech Company Co-Founder
Rushi Manche | Blockchain Tech Company Co-Founder
Rushi Manche
?
Integration of Information Security Governance and Corporate Governance
Integration of Information Security Governance and Corporate Governance
Tokyo Security Community
?
_Naver Accounts in 2025 ¨C Unlocking Smart Access to South Korea¡¯s Digital Wor...
_Naver Accounts in 2025 ¨C Unlocking Smart Access to South Korea¡¯s Digital Wor...
usashopsmm.com
?
Number Of Major Ports In India 2025.docx
Number Of Major Ports In India 2025.docx
thetradevision0
?
Oleksandr Osypenko: §µ§á§â§Ñ§Ó§Ý?§ß§ß§ñ §à§Ò§ã§ñ§Ô§à§Þ (Scope) (UA)
Oleksandr Osypenko: §µ§á§â§Ñ§Ó§Ý?§ß§ß§ñ §à§Ò§ã§ñ§Ô§à§Þ (Scope) (UA)
Lviv Startup Club
?
QuickBooks Keeps Freezing: Causes & Solutions.pptx
QuickBooks Keeps Freezing: Causes & Solutions.pptx
robastwilliams
?
IEA_Press_Release_Tullow_Agreement-16-6-2025-1.pdf
IEA_Press_Release_Tullow_Agreement-16-6-2025-1.pdf
businessweekghana
?
IT Companies in Magarpatta: A Thriving Hub of Technology and Innovation
IT Companies in Magarpatta: A Thriving Hub of Technology and Innovation
prernarathi90
?
What Drives Collectors in Sports and Beyond, and How Mantel is Bringing Them ...
What Drives Collectors in Sports and Beyond, and How Mantel is Bringing Them ...
Neil Horowitz
?
Oleksandr Osypenko: §µ§á§â§Ñ§Ó§Ý?§ß§ß§ñ §é§Ñ§ã§à§Þ §ä§Ñ §â§Ö§ã§å§â§ã§Ñ§Þ§Ú (UA)
Oleksandr Osypenko: §µ§á§â§Ñ§Ó§Ý?§ß§ß§ñ §é§Ñ§ã§à§Þ §ä§Ñ §â§Ö§ã§å§â§ã§Ñ§Þ§Ú (UA)
Lviv Startup Club
?
The Future State Of Work - Actionable Summary for Startup Founders
The Future State Of Work - Actionable Summary for Startup Founders
vikram sood
?
Improving Sales Forecasting in Volatile B2B Capital Equipment Markets - Dave ...
Improving Sales Forecasting in Volatile B2B Capital Equipment Markets - Dave ...
Dave Litwiller
?
Enterprise Architecture Professional Journal Vol IX June 2025.pdf
Enterprise Architecture Professional Journal Vol IX June 2025.pdf
Darryl_Carr
?
StarOps- AI-native platform that lets you deploy and manage production infras...
StarOps- AI-native platform that lets you deploy and manage production infras...
StarOps
?
Electronic Shelf Labels & Digital Price Tags in Delhi | Foodcare
Electronic Shelf Labels & Digital Price Tags in Delhi | Foodcare
Foodcare llp
?
Essar at IEW 2025, Leading the Way to India¡¯s Green Energy Transition.
Essar at IEW 2025, Leading the Way to India¡¯s Green Energy Transition.
essarcase
?
Hire the Best Crypto Recovery Experts for Fast Recovery in 2025: Puran Crypto...
Hire the Best Crypto Recovery Experts for Fast Recovery in 2025: Puran Crypto...
henryywalker3
?
placement-brochure Great lakes Gurgaon. 2025
placement-brochure Great lakes Gurgaon. 2025
charankumarboom
?
The Science Behind Effective Lead Nurture Programs in B2B Marketing.pptx
The Science Behind Effective Lead Nurture Programs in B2B Marketing.pptx
brandonsoros91
?
Rushi Manche | Blockchain Tech Company Co-Founder
Rushi Manche | Blockchain Tech Company Co-Founder
Rushi Manche
?
Integration of Information Security Governance and Corporate Governance
Integration of Information Security Governance and Corporate Governance
Tokyo Security Community
?
_Naver Accounts in 2025 ¨C Unlocking Smart Access to South Korea¡¯s Digital Wor...
_Naver Accounts in 2025 ¨C Unlocking Smart Access to South Korea¡¯s Digital Wor...
usashopsmm.com
?
Number Of Major Ports In India 2025.docx
Number Of Major Ports In India 2025.docx
thetradevision0
?
Oleksandr Osypenko: §µ§á§â§Ñ§Ó§Ý?§ß§ß§ñ §à§Ò§ã§ñ§Ô§à§Þ (Scope) (UA)
Oleksandr Osypenko: §µ§á§â§Ñ§Ó§Ý?§ß§ß§ñ §à§Ò§ã§ñ§Ô§à§Þ (Scope) (UA)
Lviv Startup Club
?
QuickBooks Keeps Freezing: Causes & Solutions.pptx
QuickBooks Keeps Freezing: Causes & Solutions.pptx
robastwilliams
?
IEA_Press_Release_Tullow_Agreement-16-6-2025-1.pdf
IEA_Press_Release_Tullow_Agreement-16-6-2025-1.pdf
businessweekghana
?
IT Companies in Magarpatta: A Thriving Hub of Technology and Innovation
IT Companies in Magarpatta: A Thriving Hub of Technology and Innovation
prernarathi90
?
What Drives Collectors in Sports and Beyond, and How Mantel is Bringing Them ...
What Drives Collectors in Sports and Beyond, and How Mantel is Bringing Them ...
Neil Horowitz
?
Oleksandr Osypenko: §µ§á§â§Ñ§Ó§Ý?§ß§ß§ñ §é§Ñ§ã§à§Þ §ä§Ñ §â§Ö§ã§å§â§ã§Ñ§Þ§Ú (UA)
Oleksandr Osypenko: §µ§á§â§Ñ§Ó§Ý?§ß§ß§ñ §é§Ñ§ã§à§Þ §ä§Ñ §â§Ö§ã§å§â§ã§Ñ§Þ§Ú (UA)
Lviv Startup Club
?
Ad

a book

  • 1. Exercise -1(A) : If r = sinti = costj = tk, find (i) ?? ?? (ii) ?2 ? ??2 (iii)| ?? ?? | (iv)| ?2 ? ??2 | Solution : (i) ?? ?? = ? ?? (sinti = costj = tk) = costi-sinti+tk (ii) ?2 ? ??2 = ?? ?? { ?? ?? (sinti + costj + tk)} ?? ?? (cosi - sintj + tk) =-sinti-costj (iii) ?? ?? = cosi + sintj + tk | ?? ?? | = ¡Ì???2 ? + ???? ? + 12 = ¡Ì1 + 1 = ¡Ì2 (iv) | ?2 ? ??2 |=¡Ì???2 ? + ???2 ? = ¡Ì1 = 1 Solution : Let ¨Cr,be the position vector of the particle at any time t. R=xi+yj+zk =??? ? + 2???3?? + 2???3?? V= ?? ?? = ? ?? (??? + 2???3?? + 2???3??) =??? ? ? 6???3?? + 6???3?? ? = ?2 ? ??2 = ? ?? (???? ? ? 6???3?? + 6???3??) =??? ? ? 18???3?? ? 18???3?? t=0, At t=0, V=-i+6k | ?| = ¡Ì?12 + 62 = ¡Ì37 At t= 0, a= i-18 cos 0.j-18 sin 3.0k =i-0-18 | ?|= ¡Ì(1)2 + (?18)2 = ¡Ì1 + 324 = ¡Ì325