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Консультация № 202488
28.03.2022, 20:39
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13
1
Здравствуйте! Прошу помощи в следующем вопросе:нужно найти базис френе и соприкасающуюся плоскость для кривой x^2+y^2+z^2=3 x^2+y^2=2 в точке М(1,1,1). начала с плоскости. для этого я параметризовала кривую. приняла за х - t. тогда y=sqrt(2-t^2), z=1. затем нашла производные r'(t)={1, (2-t^2)^(1/2), 0}, r''(t)={0, -2/(2-t)^(3/2), 0}.списала все в матрицу и приравняла к нулю. по правилу треугольника получилось: (z-1)(-2/(2-t)^(3/2)=0. надо бы подставить координаты точки М вместо Х,Y,Z. но тут нет Х и У. что делать не знаю
Обсуждение
28.03.2022, 20:44
общий
а еще хуже получилось нерешаемое уравнение -2/(2-t)^(3/2)=0, откуда совершенно невозможно выразить t
31.03.2022, 06:25
общий
Адресаты:
Здравствуйте, Logan_Lady! Сообщите, пожалуйста, как Вы получили компоненты вектора 
Об авторе:
Facta loquuntur.
Facta loquuntur.
31.03.2022, 07:23
общий
это первая производная от r. тогда, если подставить координаты точки М, получим r(t0)={1,1,1}, r'(t0)={1,-1,0}, r''(t0)={0,-2,0} (подставляла значения вместо t). матрица {x-1, y-1, z-1}, {1,-1,0}, {0,-2,0} приравняли к нулю. все равно какое-то странное уравнение получилось -2z+z=0. так может быть?
31.03.2022, 07:42
общий
Адресаты:
Ухожу, чтоб не мешать Вам. 2 эксперта на одну задачу - слишком расточительные время-затраты. Мы и так не успеваем ответить на все Вопросы.
31.03.2022, 07:44
общий
Адресаты:
Правильно ли Вы вычислили первую производную?
Об авторе:
Facta loquuntur.
Facta loquuntur.
31.03.2022, 19:47
общий
а. торопилась, описалась r'(t)={1,-t* (2-t^2)^(-1/2), 0}. в тетради верно у меня. вектор в точке М все равно {1,-1,0}. и тот же странный результат в матрице. и еще есть вопрос: при определении вектора Френе нашла орты касательной 1/sqrt(3) {1,1,1}, нормали 1/2{0,-2,0}, бинормали 1/sqrt(2){1,-1,0}. они как-то меняют значения в зависимости от направления. не понимаю как?
31.03.2022, 20:07
общий
Адресаты:
А правильно ли Вы вычислили вторую производную?
Об авторе:
Facta loquuntur.
Facta loquuntur.
01.04.2022, 08:59
общий
Адресаты:
Я предполагаю, что в точке 
имеем 
Тогда
или
-- уравнение соприкасающейся плоскости для заданной кривой.
имеем Тогдаили
-- уравнение соприкасающейся плоскости для заданной кривой.
Об авторе:
Facta loquuntur.
Facta loquuntur.
01.04.2022, 09:01
общий
Уважаемая администрация!
Предлагаю продлить срок действия консультации на пять суток.
Предлагаю продлить срок действия консультации на пять суток.
Об авторе:
Facta loquuntur.
Facta loquuntur.
02.04.2022, 13:47
общий
это ответ
Здравствуйте, Logan_Lady!
После совместной работы в мини-форуме консультации над уравнением соприкасающейся плоскости можно сделать следующий вывод: в точке имеем Тогда
или
-- уравнение соприкасающейся плоскости для заданной кривой.
После совместной работы в мини-форуме консультации над уравнением соприкасающейся плоскости можно сделать следующий вывод: в точке
имеем Тогдаили
-- уравнение соприкасающейся плоскости для заданной кривой.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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