Understanding Vectors in 3-Dimensional Space: Algebraic and Geometric Approaches
This section delves into vectors in 3-dimensional space, explaining the concept as an ordered triple of real numbers represented as . It defines the vector space R^3 as the collection of all such ordered triples, highlighting the significance of real numbers as vector components. The section further introduces the operations of vector addition and scalar multiplication, essential for manipulating vectors. By exploring both algebraic and geometric perspectives, readers will gain a comprehensive understanding of vectors in this dimensional space.
Understanding Vectors in 3-Dimensional Space: Algebraic and Geometric Approaches
E N D
Presentation Transcript
Section 9.2Vectors in 3-dim space Two approaches to vectors Algebraic Geometric
DEFINITION: A vector in 3-space is an ordered triple of real numbers <a,b,c>. The real numbers are the components of the vector. Example: A = < -3, 5, 17/3>
DEFINITION: The vector space R^3 is the collection of all order triples A = <a,b,c> where a, b and c are arbitrary real numbers. The vectors obey two operations, called addition (+) and scalar multiplication (.), which we now define.
