la_m4_handouts - MAC 2103 Module 4 Vectors in 2-Space and...

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1 1 MAC 2103 Module 4 Vectors in 2-Space and 3-Space I 2 Rev.F09 Learning Objectives In this module, we apply our earlier ideas specifically to vectors in 2-space, 2 , (in the xy-plane) in two dimensions and to vectors in 3-space, 3 ,(in the xyz-space) in three dimensions. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
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2 3 Rev.F09 Learning Objectives (Cont.) Upon completing this module, you should be able to: 1. Determine the components of a vector in 2 and 3 . 2. Perform vector addition, subtraction, and scalar multiplication in 2 and 3 . 3. Find the norm of a vector and the distance between points in 2 and 3 . 4. Find the dot product of two vectors in 2 and 3 . 5. Use the dot product to find the angle between two vectors in 2 and 3 . 6. Find the projection of a vector onto another vector in 2 and 3 , and express the original vector as a sum of two orthogonal vectors. 7. Find the distance between a point and a line in 2 and 3 . http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. 4 Rev.09 Vectors in 2 and 3 http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Introduction to Vectors (Geometric) Introduction to Vectors (Geometric) Norm of a Vector; Vector Norm of a Vector; Vector Operations Dot Product; Projections Dot Product; Projections There are three major topics in this module:
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3 5 Rev.F09 What are Vectors in 2 and 3 ? http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Vectors can be represented as directed line segments or arrows in 2 and 3 . The direction of the arrow specifies the direction of the vector. A vector that starts from an initial point A and terminates at a point B can be represented as . A vector is usually denoted in lowercase boldface type (like v ) in the textbook or with an arrow above it when we write it by hand. For example: A B A B AB ! " !! v = ! v = AB " ! "" . ! v ! " ! # ! v $ ! ! 6 Rev.F09 What are Vectors in 2 and 3 ? (Cont.) http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. The magnitude of the vector is the length of the vector . The vector of length zero is called the zero vector . Vectors with the same magnitude and same direction are equal to each other.
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