Section 9.2 Vectors in 3-dim space

Page 1 <img data-url='document/section-92-vectors-in-3-dim-space.html?page=1' data-page='1' class='cut-thumb lazyload' alt='Page 1: Section 9.2 Vectors in 3-dim space' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062222/56815ed0550346895dcd5d35/html5/thumbnails/1.jpg' width='140' height='200' /> Section 9.2Vectors in 3-dim space

Two approaches to vectors

1. Algebraic2. Geometric

Page 2 <img data-url='document/section-92-vectors-in-3-dim-space.html?page=2' data-page='2' class='cut-thumb lazyload' alt='Page 2: Section 9.2 Vectors in 3-dim space' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062222/56815ed0550346895dcd5d35/html5/thumbnails/2.jpg' width='140' height='200' /> • DEFINITION: A vector in 3-space is an ordered triple of real numbers . The real numbers are the components of the vector.

Example: A =

Page 3 <img data-url='document/section-92-vectors-in-3-dim-space.html?page=3' data-page='3' class='cut-thumb lazyload' alt='Page 3: Section 9.2 Vectors in 3-dim space' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062222/56815ed0550346895dcd5d35/html5/thumbnails/3.jpg' width='140' height='200' /> DEFINITION: The vector space R^3 is the collection of all order triples A = where a, b and c are arbitrary real numbers. The vectors obey two operations, called addition (+) and scalar multiplication (.), which we now define.

Page 4 <img data-url='document/section-92-vectors-in-3-dim-space.html?page=4' data-page='4' class='cut-thumb lazyload' alt='Page 4: Section 9.2 Vectors in 3-dim space' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062222/56815ed0550346895dcd5d35/html5/thumbnails/4.jpg' width='140' height='200' /> Page 5 <img data-url='document/section-92-vectors-in-3-dim-space.html?page=5' data-page='5' class='cut-thumb lazyload' alt='Page 5: Section 9.2 Vectors in 3-dim space' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062222/56815ed0550346895dcd5d35/html5/thumbnails/5.jpg' width='140' height='200' /> Page 6 <img data-url='document/section-92-vectors-in-3-dim-space.html?page=6' data-page='6' class='cut-thumb lazyload' alt='Page 6: Section 9.2 Vectors in 3-dim space' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062222/56815ed0550346895dcd5d35/html5/thumbnails/6.jpg' width='140' height='200' /> More definitions

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Section 9.2 Vectors in 3-dim space

Documents

dim space section

vector space r

arbitrary real numbers

fundamental construction

ordered triple of real

dim spacetwo approaches

scalar multiplication

order triples