Linjer i planen (2D)Plot af ret linje givet ved en parameterfremstillingEksempel 93 side 117 i Grundbog AParameterfremstilling: 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view angiver man det viste omr\303\245de i planen.Med 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 angiver man de v\303\246rdier, som parameteren LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= skal genneml\303\270be.\303\230nske en hel linje, skal parameteromr\303\245det v\303\246re tilstr\303\246kkeligt stort!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 er linjen kun tegnet for parameteren LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSIxRidGLy1GLDYtUSYmbGVxO0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yNzc3Nzc4ZW1GJy9GRUZOLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0ZKRkZGLw==, dvs. man f\303\245r et linjestykke: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Plot af ret linje givet ved en ligningEksempel 92 side 117 i Grundbog ALigning: 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRJnBsb3RzRidGL0YyL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIjpGJ0Y9LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQ=Ogs\303\245 her skal omr\303\245derne 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 v\303\246re store nok, s\303\245 man f\303\245r d\303\246kket det viste omr\303\245de 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fra parameterfremstilling til ligningEksempel 93 side 117 i Grundbog AParameterfremstilling: 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Linjens ligning er 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 eller 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2: lad LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2KFEieUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GJy8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRictSSNtb0dGJDYwUSI9RidGL0Y0L0Y4RjxGOi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZTLUYsNihRInRGJ0YvRjJGNEY3RjpGL0Y0RkFGOg==:LUkmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC1JJXN1YnNHRiU2JC9JInlHRidJInRHRidJIkxHRidJInhHRic=Konklusion: En anden mulig parameterfremstilling for linjen er 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metode:Ligning: 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Normalvektoren er 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s\303\245 er en retningsvektor 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punkt p\303\245 linjen er f.eks. (2,0).Konklusion: En tredje mulig parameterfremstilling for linjen er 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