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ET-314 Week 11 Nov 7, 2014 Topic(s): 19.1 Vectors

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Vectors

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Practice Problems: x = 3 y = 6 r = __________ = __________ x = -2 y = 5 r = __________ = __________ r = 6 = 25 x = __________ y = __________ r = 5 = -65 x = __________ y = __________

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Vector Additions In rectangular coordinates: V1 = (0.8, -0.7) V2 = (0.6, 1) V3 = V1 + V2 = ({0.8 + 0.6}, {-0.7 + 1}) = (1.4, 0.3)

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Vector Additions In polar coordinates: V1 = (0.8 60 ) = (0.8 cos(60 ), 0.8 sin(60 )) = (0.4000, 0.6928) V2 = (0.7 -30 ) = (0.7 cos(-30 ), 0.7 sin(-30 )) = (0.6062,-0.3500) V3 = V1 + V2 = (1.0062, 0.3428) = (1.0062 2 + 0.3428 2 ) 0.5 tan -1 (0.34282 / 1.00622) = 1.0630 18.8141

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V1 + V2 Vector Subtractions In rectangular coordinates: V1 = (0.8, -0.7) V2 = (0.6, 1) V3 = V1 V2 = V1 + (-V2) = (0.8, -0.7) + (-0.6, -1) = ({0.8 0.6}, {-0.7 1}) = (0.1, -1.6) V1 V2

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Practice Problems x = 2 y = 3 r = = x = 2 y = -5 r = = r = 20 = -128 x = y = r = 3 = 165 x = y =

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Practice Problems V1 = (0.8, 0.5), V2 = (0.7, -0.3), V3 = (0.6 50 ), V1 + V2 – V3 = ? More practice problems:

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S p. 702: 1-19 odd, 25-29 odd, 37-47 odd. Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle) Polar.

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