3.1_3.2 - MATH1850U/2050U: Chapter 3 EUCLIDEAN VECTOR...

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MATH1850U/2050U: Chapter 3 1 EUCLIDEAN VECTOR SPACES Vectors in 2-Space, 3-Space, and n-Space (3.1; pg. 119) Definition: Quantities that are completely determined by a number are called scalars . Quantities that need both magnitude and direction to be completely determined are called vectors . Definition: Vectors are often represented by the coordinates of the terminal point of a vector. These are called the components of the vector . Example: Definition: If n is a positive integer, then an ordered n -tuple is a sequence of n real numbers ) , , , ( 2 1 n a a a . The set of all ordered n -tuples is called n -space and is denoted n R . Applications: Vectors can be useful in representing data sets, e.g. Temperature of a fluid at certain times Positions of cars on a road
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MATH1850U/2050U: Chapter 3 2 Definition: Two vectors ) , , , ( 2 1 n u u u u and ) , , , ( 2 1 n v v v v in n R are called equal if n n v u v u v u , , , 2 2 1 1 Example: If ) , 3 , 8 , 5 ( ) 7 , 3 , , 5 ( b a , find a and b . Definition: We have the following definitions for vector arithmetic in n R : sum : ) , , , ( 2 2 1 1 n n w v w v w v w v scalar multiple : ) , , , ( 2 1 n kv kv kv k v negative : ) , , , ( 2 1 n v v v v difference : ) , , , ( 2 2 1 1 n n v w v w v w v w In Maple: > with(Student[LinearAlgebra]): > VectorSumPlot(<1,2>,<3,-5>);
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This note was uploaded on 10/12/2011 for the course MATH 1020 taught by Professor Paulatu during the Spring '11 term at UOIT.

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3.1_3.2 - MATH1850U/2050U: Chapter 3 EUCLIDEAN VECTOR...

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