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Published byLoraine Rich Modified over 9 years ago
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Vectors in the Plane and in Three-Dimensional Space
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Points in Three-Dimensional Space y x z (2,3,4)
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Distance Between Two Points
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Open Ball ofof
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Closed Ball ofof
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Directed Line Segment A B
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Opposite A B
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Example
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Definition of Vector
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Example
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Definition of Vector A vector is a quantity that is determined by a magnitude and a direction.
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Speed vs. Velocity
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Vector and Scalar Quantities Velocity Displacement Momentum Force Torque Acceleration Speed Distance Voltage Temperature Time Volume Mass
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Computer Graphics Robot Arms
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Cartesian Coordinate Represenatation of a Vector
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Find the coordinate representation.
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(3,2)
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Cartesian Coordinate Represenatation of a Vector
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Definition
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Vector Addition y x z (2,3,4) (1,-2,2)
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Vector Addition y x z (2,3,4) (1,-2,2) (3,1,6)
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Vector Addition y x z (2,3,4) (1,-2,2) (3,1,6)
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Vector Addition y x z (2,3,4) (1,-2,2) (3,1,6)
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Vector Subtraction
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Zero Vector
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Scalar Multiplication
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x y z
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Length of a Vector
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Special Unit Vectors
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x y z i j k
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Unit Vector Representation y x z
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Direction of a Vector
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Parallel Vectors
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The Triangle Inequality
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Properties
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Application
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Problems Show that the diagonals of a parallelogram bisect each other. Show that the line through the midpoints of adjacent sides of a parallelogram bisect one of the diagonals in the ratio 1:3. Show that the quadrilateral whose vertices are the midpoints of the sides of an arbitrary quadrilateral is a parallelogram.
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