III year Exam Papers with proposed code
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Le téléchargement nécessite un accès à la bibliothèque YouScribe Tout savoir sur nos offres
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.
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- paper code title of the paper date
- slur 10 urdu
- management accounting
- military operations
- b. sc
- b.sc
- 2 india
- india
- economics
- s.
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 oraMultiply a vector by a scalar – creates parallel vectors 1 2a−2a
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 system2 Start with 2-D only:Vectors inRSymbol: P(x,y andQ(x,y) PQ where1 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 ofPQ ifP(4,−3) andQ(−2,−1) What aboutQP? Find the pointQ ifP(2,−4) andPQ=4,−5 Find the pointP 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 =4,1Multiply a vector by a scalar a ca=c a,a=ca,c21 2 1 Creates parallel vectors If c > 0, they have the same direction If c < 0, they have the opposite direction 1 −b 2a2
a=a, and b=b,b General:1a22 1 Example:a=2,−b3 and =4,1Add or subtract two vectors a±a b=1,a±b,b=a±b,a±b2 1 2 1 1 2 2 a+b2a−0.5b
b General:a=a,a and b=b,21 2 1 Example:a=2,−b3 and =4,1Length 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,−3Find 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 of30with the horizontal. Find the force vectorF. 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?
