meeting 23 vectors. vectors in 2-space, 3-space, and n- space we will denote vectors in boldface...
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Meeting 23Vectors
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Vectors in 2-Space, 3-Space, and n-Space
We will denote vectors in boldface type such as a, b, v, w, and x, and we will denote scalars in lowercase italic type such as a, k, v, w, and x. When we want to indicate that a vector v has initial point A and terminal point B.
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Vector addition as a process of translating points
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Vector Subtraction
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Scalar Multiplication
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Vectors in CoordinateSystems
We will write v = (v1, v2) to denote a vector v in2-space with components (v1, v2), and v = (v1, v2, v3) to denote a vector v in 3-spacewith components (v1, v2, v3).
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Vectors Whose Initial PointIs Not at the Origin
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n-Space
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Operations on Vectors in
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Example
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The Properties of Vector Operations
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Norm of a Vector
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The Properties of a Norm
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Unit Vectors
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Example
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Dot Product
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Angle between two vectors
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Component Form of theDot Product
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Algebraic Properties of theDot Product
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Cauchy–Schwarz Inequalityand Angles in
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Exercises
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