This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Physics 2306 M. Blecher August 18, 2009 Chapter 1 Vectors 1.1 Representation of Vectors Vectors in three dimensional (3D) space are quantities possessing magnitude and direction. They are written in bold font in this note. In component form,vector A is written, A = 3 summationdisplay i =1 A i e i , (1.1) where A i is the component of the vector along the direction of the unit vector e i . The units [A] of the vector go with each component. Thus if A is a force, [ A i ]=Newtons (N). The unit vectors have magnitude of one, do not possess units, and specify one of the three mutually perpendicular directions of a righthanded system of axes in 3D. Thus unit vectors obey the scalar and vector product rules, e i e j = ij , (1.2) e i e j = 3 summationdisplay k =1 ijk e k . (1.3) In Equation 1.2, ij = (0 , 1) if ( i negationslash = j, i = j ). In Equation 1.3, ijk = (0 , 1) if (two or three indices are equal, indices all different). By definition 123 1 and an interchange of two indices causes multiplication by 1. With these 1 rules the scalar and vector products of any two vectors are, A B = 3 summationdisplay i =1 A i B i = AB cos , (1.4) A B = 3 summationdisplay ijk =1 ijk A i B j e k = AB sin n , (1.5) where A = radicalBig 3 i =1 A 2 i , B = radicalBig 3 i =1 B 2 i , is the angle between the vectors, and n A , B ....
View
Full
Document
This note was uploaded on 12/24/2011 for the course PHYS 2306 taught by Professor Ykim during the Fall '06 term at Virginia Tech.
 Fall '06
 YKim
 Physics

Click to edit the document details