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Chapter 10 Vocabulary

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Section 10.1 Vocabulary

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Three-dimensional coordinate system A coordinate system with three axis x, y, and z.

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Coordinate planes in 3 space xy-plane xz- plane yz- plane

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Octant 8 octants (sections of the graph) in a three- dimensional coordinate system.

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Distance formula in space D = √[(x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 + (z 2 – z 1 ) 2 ]

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Midpoint formula in Space ([x 1 + x 2 ]/2, [y 1 + y 2 ]/2, [z 1 + z 2 ]/2 )

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Section 10.2 Vocabulary

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Zero Vector Denoted 0 =

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Unit vectors i = j = k =

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Standard unit vector notation for v v = v 1 i + v 2 j + v 3 k

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Component form If v is represented by the directed line segment from P to Q the component form of the vector is produced by subtracting the coordinates of the initial point from the coordinates of the terminal point. V =

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Equal Two vectors are equal iff their corresponding components are equal

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Magnitude The magnitude or length of u = is ||u|| = √ u u u 3 2

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Unit vector u in the direction of v U = v / ||v||

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Sum of two vectors u = and v = u + v =

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Scalar multiple The scalar multiple of the real number c and u = is cu =

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Dot product The dot product of u = and v = is u ∙ v = u 1 v 1 + u 2 v 2 + u 3 v 3

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Angle between two vectors If Ѳ is the angle between two nonzero vectors u and v, then cos Ѳ = (u∙ v) / ||u|| ||v||

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Collinear The points P, Q, and R are collinear iff the vectors PQ and PR are parallel.

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