III year Exam Papers with proposed code

Terri Bourdon

Description

THIRUVALLUVAR UNIVERSITY, VELLORE – 632 106. TIME TABLE / CBCS NOVEMBER / DECEMBER 2011 FN : 10.00 AM TO 1.00 PM AN : 2.00 PM TO 5.00 PM - 1 - FOUNDATION PAPERS S.NO. PAPER CODE TITLE OF THE PAPER DATE & SESSION I YEAR (I SEMESTER) PART I 1. SLT 10 Tamil I (All UG Courses) 12.12.2011 FN 2. SLFR 10 French I (All UG Courses) (from 2011-2012 batch onwards) 12.12.2011 FN 3.

• paper code title of the paper date
• slur 10 urdu
• management accounting
• military operations
• b. sc
• b.sc
• 2 india
• india
• economics
• s.

Sujets

• Paper
• Industrial organization
• Thiruvalluvar University
• Skill
• Companies law
• Economics
• Military
• Accountancy
• International

Informations

• Publié par: rehoh
• Nombre de lectures: 21
• Langue: English

Extrait

Vector Geometry  What is a vector?  Definition: A directed line segment

 Characteristics:  Tail (initial point)  Tip (terminal point)  Vectors vs. Scalars  A vector has:   A vector is used to represent quantities like:    A scalar has:   A scalar is used to represent quantities like: 



Pure Geometry vs. Analytic Geometry  Pure geometry: Free Vectors    Symbol: v ora    Multiply a vector by a scalar – creates parallel vectors    1 2a  − 2 a     

     



  Add two vectors: a+b  

 Two methods: Triangle (tail to tip) Parallelogram (tail to tail)           Subtract two vectors: a−b=a+(−b)          Ex: a−2b    

Analytic geometry: Place vectors in a coordinate system 2 Start with 2-D only: Vectors inR   Symbol:  P(x,y andQ(x,y) PQ  where 1 1 ) 2 2   

  Components:    Writing a vector in terms of its components:  P(−1, 3) Q(2,−2)    v=PQ   Equal vectors:

 Find the components of PQ ifP(4,−3) andQ(−2,−1)        What about QP ?       Find the point Q ifP(2,−4) andPQ=4,−5             Find the point P ifQ(1,−1) andPQ=2, 3          

Operations on Vectors:    a=a,ab and =b,b General: 1 2 1 2     Example: a=2,−b3 and =4,1    Multiply a vector by a scalar  a ca=c a,a=ca,c 2  1 2 1   Creates parallel vectors If c > 0, they have the same direction If c < 0, they have the opposite direction   1 −b 2a  2  





   a=a, and b=b,b General: 1 a 22 1     Example: a=2,−b3 and =4,1    Add or subtract two vectors    a±a b= 1 ,a±b,b=a±b,a±b  2 1 2 1 1 2 2      a+b  2a−0.5b       



  b General: a=a,a and b=b, 2  1 2 1    Example: a=2,−b3 and =4,1    Length of a vector (also called magnitude or norm):  a       Direction of a vector: 1  a  a        “Factor” a vector:       

Find a vector having length 2 and the same direction as  a=2,−3                   Find a vector having length 4 and the opposite direction of  b=4,1                

Three Ways to Represent a Vector in 2-D  In terms of Components      In terms of Length and Direction       In terms of an Angle:  θis the angle thatvmakes with the positive x-axis   

  



Applications:  A force of 8 pounds is applied to an object making an angle  0 of 30 with the horizontal. Find the force vector F .            5π Force A has a magnitude of 20 N and points in a direction of 6 radians from the positive x axis. Force B has a magnitude of 6 N at 5π an angle of radians. What is the resultant force 4 A + B?          