# Calc10_2 - 10.2 Vectors in a Plane Mesa Verde National Park...

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10.2 Vectors in a Plane Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2003 Mesa Verde National Park, Colorado

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Warning: Only some of this is review .
Quantities that we measure that have magnitude but not direction are called scalars . Quantities such as force, displacement or velocity that have direction as well as magnitude are represented by directed line segments . A B initial point terminal point AB uuu v The length is AB uuu v

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A B initial point terminal point AB uuu v A vector is represented by a directed line segment. Vectors are equal if they have the same length and direction (same slope).
A vector is in standard position if the initial point is at the origin. x y ( 29 1 2 , v v The component form of this vector is: 1 2 , v v = v

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A vector is in standard position if the initial point is at the origin. x y ( 29 1 2 , v v The component form of this vector is: 1 2 , v v = v The magnitude (length) of 1 2 , v v = v is: 2 2 1 2 v v = + v
P Q (-3,4) (-5,2) The component form of PQ uuu v is: 2, 2 = - - v v (-2,-2) ( 29 ( 29 2 2 2 2 = - + - v 8 = 2 2 =

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If 1 = v Then v is a unit vector .
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