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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 = √[(x2 – x1)2+ (y2 – y1)2+ (z2 – z1)2]

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**Midpoint formula in Space**

([x1+ x2]/2 , [y1+ y2]/2 , [z1+ z2]/2 )

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Section 10.2 Vocabulary

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Zero Vector Denoted 0 = <0,0,0>

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Unit vectors i = <1,0,0> j = <0,1,0> k = <0,0,1>

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**Standard unit vector notation for v**

v = v1 i + v2j + v3k

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Component form If v is represented by the directed line segment from P<p1,p2,p3> to Q<q1,q2,q3> the component form of the vector is produced by subtracting the coordinates of the initial point from the coordinates of the terminal point. V = <q1-p1, q2-p2, q3-p3>

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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 = <u1,u2,u3> is**

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**Unit vector u in the direction of v**

U = v / ||v||

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Sum of two vectors u = <u1,u2,u3> and v = <v1,v2,v3> u + v = <u1 + v1 ,u2 + v2 , u3 + v3 >

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Scalar multiple The scalar multiple of the real number c and u = <u1,u2,u3> is cu = <cu1,cu2,cu3>

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Dot product The dot product of u = <u1,u2,u3> and v = <v1,v2,v3> is u ∙ v = u1 v1 + u2v2 + u3v3

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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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