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tangentplanens ligning er 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155 side 180LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==Kugle med centrum i LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JKG1mZW5jZWRHRiQ2JS1GIzYqLUkjbW5HRiQ2JVEiOUYnRjJGPC1GOTYuUSIsRidGMkY8Rj4vRkFGMUZCRkRGRkZIRkovRk1RJjAuMGVtRicvRlBRLDAuMzMzMzMzM2VtRictRjk2LlEqJnVtaW51czA7RidGMkY8Rj5GQEZCRkRGRkZIRkovRk1RLDAuMjIyMjIyMmVtRicvRlBGYG8tRlc2JVEiNkYnRjJGPEZaLUZXNiVRIjhGJ0YyRjxGMkY8RjJGPEYyRjw= og radius LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JI21uR0YkNiVRIjNGJ0YyRjxGMkY8.Ligning: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUklbXN1cEdGJDYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtaUdGJDYmUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSgmbWludXM7RidGOi9GPlEnbm9ybWFsRicvJSZmZW5jZUdGPC8lKnNlcGFyYXRvckdGPC8lKXN0cmV0Y2h5R0Y8LyUqc3ltbWV0cmljR0Y8LyUobGFyZ2VvcEdGPC8lLm1vdmFibGVsaW1pdHNHRjwvJSdhY2NlbnRHRjwvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZWLUkjbW5HRiQ2JVEiOUYnRjpGREY6RkRGOkZELUYjNiYtRlo2JVEiMkYnRjpGREY3RjpGPS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRkE2LlEiK0YnRjpGREZGRkhGSkZMRk5GUEZSRlRGVy1GLDYlLUYvNiUtRiM2Jy1GNDYmUSJ5RidGN0Y6Rj1GX28tRlo2JVEiNkYnRjpGREY6RkRGOkZERmduRlxvRl9vLUYsNiUtRi82JS1GIzYnLUY0NiZRInpGJ0Y3RjpGPUZALUZaNiVRIjhGJ0Y6RkRGOkZERjpGREZnbkZcby1GQTYuUSI9RidGOkZERkZGSEZKRkxGTkZQRlIvRlVRLDAuMjc3Nzc3OGVtRicvRlhGXnEtRiw2JS1GWjYlUSIzRidGOkZERmduRlxvRjpGRA==2 planer med ligningerne: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Beregner afstanden fra LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn til planerne: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Da afstanden fra LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRLlsyMDQsMjU1LDI1NV1GJy8lJ29wYXF1ZUdGMS8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyRjVGNy9GO1Enbm9ybWFsRic= til planen \316\261 er lig med kuglens radius, vil planen \316\261 tangere kuglen.Da afstanden fra LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRLlsyMDQsMjU1LDI1NV1GJy8lJ29wYXF1ZUdGMS8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyRjVGNy9GO1Enbm9ybWFsRic= til planen \316\262 ikke er lig med kuglens radius, vil planen \316\261 ikke tangere kuglen.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Eksempel 156 side 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mellem linjen og 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