vectors - Physics 2306 M. Blecher August 18, 2009 Chapter 1...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the 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 right-handed 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.

Page1 / 6

vectors - Physics 2306 M. Blecher August 18, 2009 Chapter 1...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online