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Консультация № 195828
11.06.2019, 12:46
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Для кривой x=(t^3-1)/t , y=(t+1)/t^2, z=t^3+1 вычислить единичные векторы касательной, бинормали, главной нормали, вывести уравнения бинормали и спрямляющей плоскости в точке M(0,2,2).
Для кривой x=(t^3-1)/t , y=(t+1)/t^2, z=t^3+1 вычислить единичные векторы касательной, бинормали, главной нормали, вывести уравнения бинормали и спрямляющей плоскости в точке M(0,2,2).
Обсуждение
12.06.2019, 19:29
общий
это ответ
Здравствуйте, darya-ser-frolova19!
Точке
соответствует значение параметра 
поэтому
-- направляющий вектор касательной к кривой в точке
согласно формуле (1) [1, с. 133];
-- единичный вектор касательной к кривой в точке
согласно формулам (2), (3) [1, с. 512], (1) [1, с. 524];
-- направляющий вектор бинормали к кривой в точке согласно формуле (2) [1, с. 522];
-- единичный вектор бинормали к кривой в точке согласно формуле (3) [1, с. 524];
-- направляющий вектор главной нормали к кривой в точке согласно формуле (3) [1, с. 522];
-- единичный вектор главной нормали к кривой в точке согласно формуле (1) [1, с. 524];
или
-- уравнение бинормали к кривой в точке согласно формуле (1) [1, с. 180];
спрямляющая плоскость кривой в точке
проходит через касательную и бинормаль [1, с. 522]; поэтому её нормальным вектором является направляющий вектор главной нормали к кривой в точке 
Выведем её уравнение.
Литература
Выгодский М. Я. Справочник по высшей математике. -- М.: Наука, 1976. -- 872 с.
Точке
соответствует значение параметра поэтому-- направляющий вектор касательной к кривой в точке
согласно формуле (1) [1, с. 133];
-- единичный вектор касательной к кривой в точке
согласно формулам (2), (3) [1, с. 512], (1) [1, с. 524];-- направляющий вектор бинормали к кривой в точке
согласно формуле (2) [1, с. 522];-- единичный вектор бинормали к кривой в точке
согласно формуле (3) [1, с. 524];-- направляющий вектор главной нормали к кривой в точке
согласно формуле (3) [1, с. 522];-- единичный вектор главной нормали к кривой в точке
согласно формуле (1) [1, с. 524];или
-- уравнение бинормали к кривой в точке
согласно формуле (1) [1, с. 180];спрямляющая плоскость кривой в точке
проходит через касательную и бинормаль [1, с. 522]; поэтому её нормальным вектором является направляющий вектор главной нормали к кривой в точке Выведем её уравнение.Литература
Выгодский М. Я. Справочник по высшей математике. -- М.: Наука, 1976. -- 872 с.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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