Garza Floyd
08/20/2024 · Senior High School
3. Вычислите \( \vec{a} \cdot \vec{b},(\vec{a} \vec{b} \vec{c}) \), если \( \vec{a}(-5 ; 1 ; 4), \vec{b}(6 ;-2 ; 3), \vec{c}(3 ;-4 ; 6) \) 4. Составьте уравнение прямой, содержащей высоту BH , если \( \mathrm{A}(3 ; 5), \mathrm{B}(5 ; 2), \mathrm{C}(1 ; 1) \).
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**3. Вычисление скалярного и тройного произведений:**
Даны векторы:
\[
\vec{a} = (-5;\, 1;\, 4), \quad \vec{b} = (6;\, -2;\, 3), \quad \vec{c} = (3;\, -4;\, 6)
\]
- **Скалярное произведение \(\vec{a} \cdot \vec{b}\):**
\[
\vec{a} \cdot \vec{b} = (-5) \times 6 + 1 \times (-2) + 4 \times 3 = -30 - 2 + 12 = -20
\]
- **Тройное скалярное произведение \((\vec{a} \, \vec{b} \, \vec{c})\):**
\[
(\vec{a} \, \vec{b} \, \vec{c}) = -99
\]
**Ответ:**
\[
\vec{a} \cdot \vec{b} = -20, \quad (\vec{a} \, \vec{b} \, \vec{c}) = -99
\]
---
**4. Уравнение высоты BH в треугольнике ABC:**
Даны точки:
\[
A(3;\, 5), \quad B(5;\, 2), \quad C(1;\, 1)
\]
- **Уравнение прямой AC:**
\[
y = 2x - 1
\]
- **Уравнение высоты BH:**
\[
x + 2y = 9
\]
**Ответ:**
\[
\text{Уравнение высоты } BH: \quad x + 2y = 9
\]
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