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Консультация № 189051
31.03.2016, 10:45
0.00 руб.
31.03.2016, 14:08
1
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
задание 4 вопрос 44
Найти единичный вектор, перпендикулярный векторам AB и AC и образующий с осью Oy тупой угол, если заданы точки A(3; -1; -2), B(6; 3; -4), C(5; -2; -4).
спасибо заранее)))
задание 4 вопрос 44
Найти единичный вектор, перпендикулярный векторам AB и AC и образующий с осью Oy тупой угол, если заданы точки A(3; -1; -2), B(6; 3; -4), C(5; -2; -4).
спасибо заранее)))
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Обсуждение
31.03.2016, 14:43
общий
это ответ
Здравствуйте, Katerina!
1. Вычислим координаты векторов AB и AC:
2. Вычислим координаты псевдовектора ABxAC - векторного произведения векторов AB и AC:
3. Вычислим длину псевдовектора ABxAC:
4. Вычислим координаты орта направления псевдовектора ABxAC:
5. Находим скалярное произведение орта направления псевдовектора ABxAC и орта направления оси Oy:
Скалярное произведение получилось положительным, что соответствует острому углу между скалярно перемножаемыми векторами. Значит, тупой угол с осью Oy образуют вектор -(ABxAC) и орт его направления, т. е. вектор
Ответ: {10/15; -2/15; 11/15}.
С уважением.
1. Вычислим координаты векторов AB и AC:
AB={6-3; 3-(-1); -4-(-2)}={3; 4; -2},
AC={5-3; -2-(-1); -4-(-2)}={2; -1; -2}.
2. Вычислим координаты псевдовектора ABxAC - векторного произведения векторов AB и AC:
ABxAC=i(4*(-2)-(-2)*(-1))-j(3*(-2)-(-2)*2)+k(3*(-1)-4*2)=
=-10i+2j-11k={-10; 2; -11}.
3. Вычислим длину псевдовектора ABxAC:
|ABxAC|=[$8730$]((-10)[sup]2[/sup]+2[sup]2[/sup]+(-11)[sup]2[/sup])=[$8730$]225=15.
4. Вычислим координаты орта направления псевдовектора ABxAC:
e[sub]ABxAC[/sub]=(ABxAC)/|ABxAC|={-10/15; 2/15; -11/15}.
5. Находим скалярное произведение орта направления псевдовектора ABxAC и орта направления оси Oy:
e[sub]ABxAC[/sub][$149$]j=-10/15*0+2/15*1+(-11/15)*0=2/15.
Скалярное произведение получилось положительным, что соответствует острому углу между скалярно перемножаемыми векторами. Значит, тупой угол с осью Oy образуют вектор -(ABxAC) и орт его направления, т. е. вектор
-e[sub]ABxAC[/sub]={10/15; -2/15; 11/15}.
Ответ: {10/15; -2/15; 11/15}.
С уважением.
5
супер спасибо
Об авторе:
Facta loquuntur.
Facta loquuntur.
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