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Section 9.2 Vectors in 3-dim space

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Section 9.2 Vectors 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>. - PowerPoint PPT Presentation

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Section 9.2 Vectors in 3-dim space Two approaches to vectors 1.Algebraic 2.Geometric

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Page 1: Section 9.2 Vectors in 3-dim space

Section 9.2Vectors in 3-dim space

Two approaches to vectors

1. Algebraic2. Geometric

Page 2: Section 9.2 Vectors in 3-dim space

• 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>

Page 3: Section 9.2 Vectors in 3-dim space

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.

Page 4: Section 9.2 Vectors in 3-dim space

Page 5: Section 9.2 Vectors in 3-dim space

Page 6: Section 9.2 Vectors in 3-dim space

More definitions

Page 7: Section 9.2 Vectors in 3-dim space

More definitions

Page 8: Section 9.2 Vectors in 3-dim space

More definitions

Page 9: Section 9.2 Vectors in 3-dim space

More definitions

Page 10: Section 9.2 Vectors in 3-dim space

More definitions

Page 11: Section 9.2 Vectors in 3-dim space

A fundamental construction*

Page 12: Section 9.2 Vectors in 3-dim space

A fundamental construction*

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